Basic Theory of Algebraic Groups and Lie Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1981
|
| Schriftenreihe: | Graduate Texts in Mathematics
75 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely self-contained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counter-examples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to re-iterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley |
| Beschreibung: | 1 Online-Ressource (267p) |
| ISBN: | 9781461381143 9781461381167 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4613-8114-3 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042420665 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1981 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461381143 |c Online |9 978-1-4613-8114-3 | ||
| 020 | |a 9781461381167 |c Print |9 978-1-4613-8116-7 | ||
| 024 | 7 | |a 10.1007/978-1-4613-8114-3 |2 doi | |
| 035 | |a (OCoLC)863785686 | ||
| 035 | |a (DE-599)BVBBV042420665 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 512.2 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Hochschild, Gerhard P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Basic Theory of Algebraic Groups and Lie Algebras |c by Gerhard P. Hochschild |
| 264 | 1 | |a New York, NY |b Springer New York |c 1981 | |
| 300 | |a 1 Online-Ressource (267p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 75 |x 0072-5285 | |
| 500 | |a The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely self-contained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counter-examples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to re-iterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Topological Groups | |
| 650 | 4 | |a Group Theory and Generalizations | |
| 650 | 4 | |a Topological Groups, Lie Groups | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Lie-Algebra |0 (DE-588)4130355-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Gruppe |0 (DE-588)4001164-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare algebraische Gruppe |0 (DE-588)4295326-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lie-Algebra |0 (DE-588)4130355-6 |D s |
| 689 | 0 | 1 | |a Algebraische Gruppe |0 (DE-588)4001164-1 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Lineare algebraische Gruppe |0 (DE-588)4295326-1 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4613-8114-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856082 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153092834328576 |
|---|---|
| any_adam_object | |
| author | Hochschild, Gerhard P. |
| author_facet | Hochschild, Gerhard P. |
| author_role | aut |
| author_sort | Hochschild, Gerhard P. |
| author_variant | g p h gp gph |
| building | Verbundindex |
| bvnumber | BV042420665 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863785686 (DE-599)BVBBV042420665 |
| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-8114-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03615nmm a2200553zcb4500</leader><controlfield tag="001">BV042420665</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1981 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461381143</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4613-8114-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461381167</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4613-8116-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4613-8114-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863785686</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420665</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.2</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hochschild, Gerhard P.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Basic Theory of Algebraic Groups and Lie Algebras</subfield><subfield code="c">by Gerhard P. Hochschild</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1981</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (267p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">75</subfield><subfield code="x">0072-5285</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely self-contained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counter-examples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to re-iterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological Groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group Theory and Generalizations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological Groups, Lie Groups</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lie-Algebra</subfield><subfield code="0">(DE-588)4130355-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Gruppe</subfield><subfield code="0">(DE-588)4001164-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lineare algebraische Gruppe</subfield><subfield code="0">(DE-588)4295326-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Lie-Algebra</subfield><subfield code="0">(DE-588)4130355-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Algebraische Gruppe</subfield><subfield code="0">(DE-588)4001164-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Lineare algebraische Gruppe</subfield><subfield code="0">(DE-588)4295326-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4613-8114-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856082</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042420665 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461381143 9781461381167 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856082 |
| oclc_num | 863785686 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (267p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Graduate Texts in Mathematics |
| spelling | Hochschild, Gerhard P. Verfasser aut Basic Theory of Algebraic Groups and Lie Algebras by Gerhard P. Hochschild New York, NY Springer New York 1981 1 Online-Ressource (267p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 75 0072-5285 The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely self-contained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counter-examples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to re-iterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley Mathematics Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Algebraische Gruppe (DE-588)4001164-1 s 1\p DE-604 Lineare algebraische Gruppe (DE-588)4295326-1 s 2\p DE-604 https://doi.org/10.1007/978-1-4613-8114-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hochschild, Gerhard P. Basic Theory of Algebraic Groups and Lie Algebras Mathematics Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd Algebraische Gruppe (DE-588)4001164-1 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4001164-1 (DE-588)4295326-1 |
| title | Basic Theory of Algebraic Groups and Lie Algebras |
| title_auth | Basic Theory of Algebraic Groups and Lie Algebras |
| title_exact_search | Basic Theory of Algebraic Groups and Lie Algebras |
| title_full | Basic Theory of Algebraic Groups and Lie Algebras by Gerhard P. Hochschild |
| title_fullStr | Basic Theory of Algebraic Groups and Lie Algebras by Gerhard P. Hochschild |
| title_full_unstemmed | Basic Theory of Algebraic Groups and Lie Algebras by Gerhard P. Hochschild |
| title_short | Basic Theory of Algebraic Groups and Lie Algebras |
| title_sort | basic theory of algebraic groups and lie algebras |
| topic | Mathematics Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd Algebraische Gruppe (DE-588)4001164-1 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| topic_facet | Mathematics Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Algebra Algebraische Gruppe Lineare algebraische Gruppe |
| url | https://doi.org/10.1007/978-1-4613-8114-3 |
| work_keys_str_mv | AT hochschildgerhardp basictheoryofalgebraicgroupsandliealgebras |