Representations of Lie algebras :: an introduction through gln /
"This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules o...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2012.
|
| Schriftenreihe: | Australian Mathematical Society lecture series ;
22. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics"-- |
| Beschreibung: | 1 online resource (ix, 156 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139550208 1139550209 1139555162 9781139555166 9781139236126 1139236121 9781139564984 1139564986 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn808501344 | ||
| 003 | OCoLC | ||
| 005 | 20240705115654.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 120828s2012 enka ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d E7B |d OCLCQ |d MHW |d YDXCP |d OCLCO |d CAMBR |d EBLCP |d DEBSZ |d MEAUC |d UMI |d LRU |d OCLCQ |d OCLCF |d OCLCQ |d HEBIS |d OCLCO |d UAB |d OCLCQ |d COCUF |d CNNOR |d STF |d CEF |d CUY |d MERUC |d ZCU |d ICG |d VTS |d OCLCQ |d K6U |d LOA |d VT2 |d U3W |d AU@ |d CNCEN |d DEBBG |d OCLCQ |d WYU |d LVT |d S8J |d S9I |d TKN |d DKC |d OCLCQ |d UKAHL |d OCLCQ |d A6Q |d OCLCQ |d G3B |d OCLCQ |d UKCRE |d AJS |d OCLCQ |d OCLCO |d OCLCQ |d S9M |d OCLCL | ||
| 019 | |a 811489742 |a 815824650 |a 852166390 |a 1042918296 |a 1043673834 |a 1058558720 |a 1065686526 |a 1076626925 |a 1081208672 |a 1084359233 |a 1153548772 | ||
| 020 | |a 9781139550208 |q (electronic bk.) | ||
| 020 | |a 1139550209 |q (electronic bk.) | ||
| 020 | |a 1139555162 |q (electronic bk.) | ||
| 020 | |a 9781139555166 |q (electronic bk.) | ||
| 020 | |a 9781139236126 |q (electronic bk.) | ||
| 020 | |a 1139236121 |q (electronic bk.) | ||
| 020 | |a 9781139564984 | ||
| 020 | |a 1139564986 | ||
| 020 | |z 9781107653610 | ||
| 020 | |z 1107653614 | ||
| 020 | |z 9781139552714 | ||
| 020 | |z 1139552716 | ||
| 035 | |a (OCoLC)808501344 |z (OCoLC)811489742 |z (OCoLC)815824650 |z (OCoLC)852166390 |z (OCoLC)1042918296 |z (OCoLC)1043673834 |z (OCoLC)1058558720 |z (OCoLC)1065686526 |z (OCoLC)1076626925 |z (OCoLC)1081208672 |z (OCoLC)1084359233 |z (OCoLC)1153548772 | ||
| 037 | |a CL0500000233 |b Safari Books Online | ||
| 050 | 4 | |a QA252.3 | |
| 072 | 7 | |a MAT |x 002040 |2 bisacsh | |
| 082 | 7 | |a 512/.482 |2 23 | |
| 084 | |a MAT002000 |2 bisacsh | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Henderson, Anthony, |d 1976- |1 https://id.oclc.org/worldcat/entity/E39PCjthJTX83HjCYVWwXGBbQy |0 http://id.loc.gov/authorities/names/n2012036752 | |
| 245 | 1 | 0 | |a Representations of Lie algebras : |b an introduction through gln / |c Anthony Henderson, School of Mathematics and Statistics, University of Sydney. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource (ix, 156 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a Australian Mathematical Society lecture series ; |v 22 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Cover; Representations of Lie Algebras; AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES; Title; Copyright; Contents; Preface; Notational conventions; CHAPTER 1 Motivation: representations of Lie groups; 1.1 Homomorphisms of general linear groups; 1.2 Multilinear algebra; 1.3 Linearization of the problem; 1.4 Lie's theorem; CHAPTER 2 Definition of a Lie algebra; 2.1 Definition and first examples; 2.2 Classification and isomorphisms; 2.3 Exercises; CHAPTER 3 Basic structure of a Lie algebra; 3.1 Lie subalgebras; 3.2 Ideals; 3.3 Quotients and simple Lie algebras; 3.4 Exercises. | |
| 505 | 8 | |a CHAPTER 4 Modules over a Lie algebra; 4.1 Definition of a module; 4.2 Isomorphism of modules; 4.3 Submodules and irreducible modules; 4.4 Complete reducibility; 4.5 Exercises; CHAPTER 5 The theory of sl2-modules; 5.1 Classification of irreducibles; 5.2 Complete reducibility; 5.3 Exercises; CHAPTER 6 General theory of modules; 6.1 Duals and tensor products; 6.2 Hom-spaces and bilinear forms; 6.3 Schur's lemma and the Killing form; 6.4 Casimir operators; 6.5 Exercises; CHAPTER 7 Integral gln-modules; 7.1 Integral weights; 7.2 Highest-weight modules; 7.3 Irreducibility of highest-weight modules. | |
| 505 | 8 | |a 7.4 Tensor-product construction of irreducibles; 7.5 Complete reducibility; 7.6 Exercises; CHAPTER 8 Guide to further reading; 8.1 Classification of simple Lie algebras; 8.2 Representations of simple Lie algebras; 8.3 Characters and bases of representations; APPENDIX Solutions to the exercises; Solutions for Chapter 2 exercises; Solutions for Chapter 3 exercises; Solutions for Chapter 4 exercises; Solutions for Chapter 5 exercises; Solutions for Chapter 6 exercises; Solutions for Chapter 7 exercises; References; Index. | |
| 520 | |a "This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics"-- |c Provided by publisher | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Representations of Lie algebras. |0 http://id.loc.gov/authorities/subjects/sh2007005290 | |
| 650 | 6 | |a Représentations des algèbres de Lie. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Álgebras de Lie |2 embne | |
| 650 | 7 | |a Representations of Lie algebras |2 fast | |
| 650 | 7 | |a Lie-Algebra |2 gnd |0 http://d-nb.info/gnd/4130355-6 | |
| 650 | 7 | |a Darstellungstheorie |2 gnd |0 http://d-nb.info/gnd/4148816-7 | |
| 758 | |i has work: |a Representations of Lie algebras (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFYmWD8mcbDTFc7Yb9R6gC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Henderson, Anthony, 1976- |t Representations of Lie algebras |z 9781107653610 |w (DLC) 2012021841 |w (OCoLC)785872028 |
| 830 | 0 | |a Australian Mathematical Society lecture series ; |v 22. |0 http://id.loc.gov/authorities/names/n84705632 | |
| 856 | 1 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473268 |3 Volltext | |
| 856 | 1 | |l CBO01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473268 |3 Volltext | |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH34206421 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH33350838 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH26478999 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL989151 | ||
| 938 | |a ebrary |b EBRY |n ebr10591104 | ||
| 938 | |a EBSCOhost |b EBSC |n 473268 | ||
| 938 | |a YBP Library Services |b YANK |n 9568787 | ||
| 938 | |a YBP Library Services |b YANK |n 9914644 | ||
| 938 | |a YBP Library Services |b YANK |n 9600418 | ||
| 938 | |a YBP Library Services |b YANK |n 9621280 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn808501344 |
|---|---|
| _version_ | 1813903584992952320 |
| adam_text | |
| any_adam_object | |
| author | Henderson, Anthony, 1976- |
| author_GND | http://id.loc.gov/authorities/names/n2012036752 |
| author_facet | Henderson, Anthony, 1976- |
| author_role | |
| author_sort | Henderson, Anthony, 1976- |
| author_variant | a h ah |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA252 |
| callnumber-raw | QA252.3 |
| callnumber-search | QA252.3 |
| callnumber-sort | QA 3252.3 |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover; Representations of Lie Algebras; AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES; Title; Copyright; Contents; Preface; Notational conventions; CHAPTER 1 Motivation: representations of Lie groups; 1.1 Homomorphisms of general linear groups; 1.2 Multilinear algebra; 1.3 Linearization of the problem; 1.4 Lie's theorem; CHAPTER 2 Definition of a Lie algebra; 2.1 Definition and first examples; 2.2 Classification and isomorphisms; 2.3 Exercises; CHAPTER 3 Basic structure of a Lie algebra; 3.1 Lie subalgebras; 3.2 Ideals; 3.3 Quotients and simple Lie algebras; 3.4 Exercises. CHAPTER 4 Modules over a Lie algebra; 4.1 Definition of a module; 4.2 Isomorphism of modules; 4.3 Submodules and irreducible modules; 4.4 Complete reducibility; 4.5 Exercises; CHAPTER 5 The theory of sl2-modules; 5.1 Classification of irreducibles; 5.2 Complete reducibility; 5.3 Exercises; CHAPTER 6 General theory of modules; 6.1 Duals and tensor products; 6.2 Hom-spaces and bilinear forms; 6.3 Schur's lemma and the Killing form; 6.4 Casimir operators; 6.5 Exercises; CHAPTER 7 Integral gln-modules; 7.1 Integral weights; 7.2 Highest-weight modules; 7.3 Irreducibility of highest-weight modules. 7.4 Tensor-product construction of irreducibles; 7.5 Complete reducibility; 7.6 Exercises; CHAPTER 8 Guide to further reading; 8.1 Classification of simple Lie algebras; 8.2 Representations of simple Lie algebras; 8.3 Characters and bases of representations; APPENDIX Solutions to the exercises; Solutions for Chapter 2 exercises; Solutions for Chapter 3 exercises; Solutions for Chapter 4 exercises; Solutions for Chapter 5 exercises; Solutions for Chapter 6 exercises; Solutions for Chapter 7 exercises; References; Index. |
| ctrlnum | (OCoLC)808501344 |
| dewey-full | 512/.482 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.482 |
| dewey-search | 512/.482 |
| dewey-sort | 3512 3482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06790cam a2200805 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn808501344</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20240705115654.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">120828s2012 enka ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MHW</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCO</subfield><subfield code="d">CAMBR</subfield><subfield code="d">EBLCP</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">MEAUC</subfield><subfield code="d">UMI</subfield><subfield code="d">LRU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">HEBIS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">UAB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">COCUF</subfield><subfield code="d">CNNOR</subfield><subfield code="d">STF</subfield><subfield code="d">CEF</subfield><subfield code="d">CUY</subfield><subfield code="d">MERUC</subfield><subfield code="d">ZCU</subfield><subfield code="d">ICG</subfield><subfield code="d">VTS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">K6U</subfield><subfield code="d">LOA</subfield><subfield code="d">VT2</subfield><subfield code="d">U3W</subfield><subfield code="d">AU@</subfield><subfield code="d">CNCEN</subfield><subfield code="d">DEBBG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">LVT</subfield><subfield code="d">S8J</subfield><subfield code="d">S9I</subfield><subfield code="d">TKN</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">A6Q</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">G3B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKCRE</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">S9M</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">811489742</subfield><subfield code="a">815824650</subfield><subfield code="a">852166390</subfield><subfield code="a">1042918296</subfield><subfield code="a">1043673834</subfield><subfield code="a">1058558720</subfield><subfield code="a">1065686526</subfield><subfield code="a">1076626925</subfield><subfield code="a">1081208672</subfield><subfield code="a">1084359233</subfield><subfield code="a">1153548772</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139550208</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139550209</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139555162</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139555166</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139236126</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139236121</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781139564984</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1139564986</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781107653610</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">1107653614</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781139552714</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">1139552716</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)808501344</subfield><subfield code="z">(OCoLC)811489742</subfield><subfield code="z">(OCoLC)815824650</subfield><subfield code="z">(OCoLC)852166390</subfield><subfield code="z">(OCoLC)1042918296</subfield><subfield code="z">(OCoLC)1043673834</subfield><subfield code="z">(OCoLC)1058558720</subfield><subfield code="z">(OCoLC)1065686526</subfield><subfield code="z">(OCoLC)1076626925</subfield><subfield code="z">(OCoLC)1081208672</subfield><subfield code="z">(OCoLC)1084359233</subfield><subfield code="z">(OCoLC)1153548772</subfield></datafield><datafield tag="037" ind1=" " ind2=" "><subfield code="a">CL0500000233</subfield><subfield code="b">Safari Books Online</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA252.3</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">002040</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">512/.482</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT002000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Henderson, Anthony,</subfield><subfield code="d">1976-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjthJTX83HjCYVWwXGBbQy</subfield><subfield code="0">http://id.loc.gov/authorities/names/n2012036752</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Representations of Lie algebras :</subfield><subfield code="b">an introduction through gln /</subfield><subfield code="c">Anthony Henderson, School of Mathematics and Statistics, University of Sydney.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">2012.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (ix, 156 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">data file</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Australian Mathematical Society lecture series ;</subfield><subfield code="v">22</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Representations of Lie Algebras; AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES; Title; Copyright; Contents; Preface; Notational conventions; CHAPTER 1 Motivation: representations of Lie groups; 1.1 Homomorphisms of general linear groups; 1.2 Multilinear algebra; 1.3 Linearization of the problem; 1.4 Lie's theorem; CHAPTER 2 Definition of a Lie algebra; 2.1 Definition and first examples; 2.2 Classification and isomorphisms; 2.3 Exercises; CHAPTER 3 Basic structure of a Lie algebra; 3.1 Lie subalgebras; 3.2 Ideals; 3.3 Quotients and simple Lie algebras; 3.4 Exercises.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">CHAPTER 4 Modules over a Lie algebra; 4.1 Definition of a module; 4.2 Isomorphism of modules; 4.3 Submodules and irreducible modules; 4.4 Complete reducibility; 4.5 Exercises; CHAPTER 5 The theory of sl2-modules; 5.1 Classification of irreducibles; 5.2 Complete reducibility; 5.3 Exercises; CHAPTER 6 General theory of modules; 6.1 Duals and tensor products; 6.2 Hom-spaces and bilinear forms; 6.3 Schur's lemma and the Killing form; 6.4 Casimir operators; 6.5 Exercises; CHAPTER 7 Integral gln-modules; 7.1 Integral weights; 7.2 Highest-weight modules; 7.3 Irreducibility of highest-weight modules.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">7.4 Tensor-product construction of irreducibles; 7.5 Complete reducibility; 7.6 Exercises; CHAPTER 8 Guide to further reading; 8.1 Classification of simple Lie algebras; 8.2 Representations of simple Lie algebras; 8.3 Characters and bases of representations; APPENDIX Solutions to the exercises; Solutions for Chapter 2 exercises; Solutions for Chapter 3 exercises; Solutions for Chapter 4 exercises; Solutions for Chapter 5 exercises; Solutions for Chapter 6 exercises; Solutions for Chapter 7 exercises; References; Index.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">"This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics"--</subfield><subfield code="c">Provided by publisher</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Representations of Lie algebras.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh2007005290</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Représentations des algèbres de Lie.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Algebra</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Algebra</subfield><subfield code="x">Intermediate.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Álgebras de Lie</subfield><subfield code="2">embne</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Representations of Lie algebras</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lie-Algebra</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4130355-6</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Darstellungstheorie</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4148816-7</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Representations of Lie algebras (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFYmWD8mcbDTFc7Yb9R6gC</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Henderson, Anthony, 1976-</subfield><subfield code="t">Representations of Lie algebras</subfield><subfield code="z">9781107653610</subfield><subfield code="w">(DLC) 2012021841</subfield><subfield code="w">(OCoLC)785872028</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Australian Mathematical Society lecture series ;</subfield><subfield code="v">22.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n84705632</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473268</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473268</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH34206421</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH33350838</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH26478999</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL989151</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10591104</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">473268</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">9568787</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">9914644</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">9600418</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">9621280</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn808501344 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:21:01Z |
| institution | BVB |
| isbn | 9781139550208 1139550209 1139555162 9781139555166 9781139236126 1139236121 9781139564984 1139564986 |
| language | English |
| oclc_num | 808501344 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (ix, 156 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Australian Mathematical Society lecture series ; |
| series2 | Australian Mathematical Society lecture series ; |
| spelling | Henderson, Anthony, 1976- https://id.oclc.org/worldcat/entity/E39PCjthJTX83HjCYVWwXGBbQy http://id.loc.gov/authorities/names/n2012036752 Representations of Lie algebras : an introduction through gln / Anthony Henderson, School of Mathematics and Statistics, University of Sydney. Cambridge : Cambridge University Press, 2012. 1 online resource (ix, 156 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Australian Mathematical Society lecture series ; 22 Includes bibliographical references and index. Cover; Representations of Lie Algebras; AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES; Title; Copyright; Contents; Preface; Notational conventions; CHAPTER 1 Motivation: representations of Lie groups; 1.1 Homomorphisms of general linear groups; 1.2 Multilinear algebra; 1.3 Linearization of the problem; 1.4 Lie's theorem; CHAPTER 2 Definition of a Lie algebra; 2.1 Definition and first examples; 2.2 Classification and isomorphisms; 2.3 Exercises; CHAPTER 3 Basic structure of a Lie algebra; 3.1 Lie subalgebras; 3.2 Ideals; 3.3 Quotients and simple Lie algebras; 3.4 Exercises. CHAPTER 4 Modules over a Lie algebra; 4.1 Definition of a module; 4.2 Isomorphism of modules; 4.3 Submodules and irreducible modules; 4.4 Complete reducibility; 4.5 Exercises; CHAPTER 5 The theory of sl2-modules; 5.1 Classification of irreducibles; 5.2 Complete reducibility; 5.3 Exercises; CHAPTER 6 General theory of modules; 6.1 Duals and tensor products; 6.2 Hom-spaces and bilinear forms; 6.3 Schur's lemma and the Killing form; 6.4 Casimir operators; 6.5 Exercises; CHAPTER 7 Integral gln-modules; 7.1 Integral weights; 7.2 Highest-weight modules; 7.3 Irreducibility of highest-weight modules. 7.4 Tensor-product construction of irreducibles; 7.5 Complete reducibility; 7.6 Exercises; CHAPTER 8 Guide to further reading; 8.1 Classification of simple Lie algebras; 8.2 Representations of simple Lie algebras; 8.3 Characters and bases of representations; APPENDIX Solutions to the exercises; Solutions for Chapter 2 exercises; Solutions for Chapter 3 exercises; Solutions for Chapter 4 exercises; Solutions for Chapter 5 exercises; Solutions for Chapter 6 exercises; Solutions for Chapter 7 exercises; References; Index. "This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics"-- Provided by publisher Print version record. Representations of Lie algebras. http://id.loc.gov/authorities/subjects/sh2007005290 Représentations des algèbres de Lie. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Álgebras de Lie embne Representations of Lie algebras fast Lie-Algebra gnd http://d-nb.info/gnd/4130355-6 Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 has work: Representations of Lie algebras (Text) https://id.oclc.org/worldcat/entity/E39PCFYmWD8mcbDTFc7Yb9R6gC https://id.oclc.org/worldcat/ontology/hasWork Print version: Henderson, Anthony, 1976- Representations of Lie algebras 9781107653610 (DLC) 2012021841 (OCoLC)785872028 Australian Mathematical Society lecture series ; 22. http://id.loc.gov/authorities/names/n84705632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473268 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473268 Volltext |
| spellingShingle | Henderson, Anthony, 1976- Representations of Lie algebras : an introduction through gln / Australian Mathematical Society lecture series ; Cover; Representations of Lie Algebras; AUSTRALIAN MATHEMATICAL SOCIETY LECTURE SERIES; Title; Copyright; Contents; Preface; Notational conventions; CHAPTER 1 Motivation: representations of Lie groups; 1.1 Homomorphisms of general linear groups; 1.2 Multilinear algebra; 1.3 Linearization of the problem; 1.4 Lie's theorem; CHAPTER 2 Definition of a Lie algebra; 2.1 Definition and first examples; 2.2 Classification and isomorphisms; 2.3 Exercises; CHAPTER 3 Basic structure of a Lie algebra; 3.1 Lie subalgebras; 3.2 Ideals; 3.3 Quotients and simple Lie algebras; 3.4 Exercises. CHAPTER 4 Modules over a Lie algebra; 4.1 Definition of a module; 4.2 Isomorphism of modules; 4.3 Submodules and irreducible modules; 4.4 Complete reducibility; 4.5 Exercises; CHAPTER 5 The theory of sl2-modules; 5.1 Classification of irreducibles; 5.2 Complete reducibility; 5.3 Exercises; CHAPTER 6 General theory of modules; 6.1 Duals and tensor products; 6.2 Hom-spaces and bilinear forms; 6.3 Schur's lemma and the Killing form; 6.4 Casimir operators; 6.5 Exercises; CHAPTER 7 Integral gln-modules; 7.1 Integral weights; 7.2 Highest-weight modules; 7.3 Irreducibility of highest-weight modules. 7.4 Tensor-product construction of irreducibles; 7.5 Complete reducibility; 7.6 Exercises; CHAPTER 8 Guide to further reading; 8.1 Classification of simple Lie algebras; 8.2 Representations of simple Lie algebras; 8.3 Characters and bases of representations; APPENDIX Solutions to the exercises; Solutions for Chapter 2 exercises; Solutions for Chapter 3 exercises; Solutions for Chapter 4 exercises; Solutions for Chapter 5 exercises; Solutions for Chapter 6 exercises; Solutions for Chapter 7 exercises; References; Index. Representations of Lie algebras. http://id.loc.gov/authorities/subjects/sh2007005290 Représentations des algèbres de Lie. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Álgebras de Lie embne Representations of Lie algebras fast Lie-Algebra gnd http://d-nb.info/gnd/4130355-6 Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2007005290 http://d-nb.info/gnd/4130355-6 http://d-nb.info/gnd/4148816-7 |
| title | Representations of Lie algebras : an introduction through gln / |
| title_auth | Representations of Lie algebras : an introduction through gln / |
| title_exact_search | Representations of Lie algebras : an introduction through gln / |
| title_full | Representations of Lie algebras : an introduction through gln / Anthony Henderson, School of Mathematics and Statistics, University of Sydney. |
| title_fullStr | Representations of Lie algebras : an introduction through gln / Anthony Henderson, School of Mathematics and Statistics, University of Sydney. |
| title_full_unstemmed | Representations of Lie algebras : an introduction through gln / Anthony Henderson, School of Mathematics and Statistics, University of Sydney. |
| title_short | Representations of Lie algebras : |
| title_sort | representations of lie algebras an introduction through gln |
| title_sub | an introduction through gln / |
| topic | Representations of Lie algebras. http://id.loc.gov/authorities/subjects/sh2007005290 Représentations des algèbres de Lie. MATHEMATICS Algebra General. bisacsh MATHEMATICS Algebra Intermediate. bisacsh Álgebras de Lie embne Representations of Lie algebras fast Lie-Algebra gnd http://d-nb.info/gnd/4130355-6 Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 |
| topic_facet | Representations of Lie algebras. Représentations des algèbres de Lie. MATHEMATICS Algebra General. MATHEMATICS Algebra Intermediate. Álgebras de Lie Representations of Lie algebras Lie-Algebra Darstellungstheorie |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=473268 |
| work_keys_str_mv | AT hendersonanthony representationsofliealgebrasanintroductionthroughgln |