Complex semisimple Lie algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Edition: | Reprint of the 1987 ed. |
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | IX, 74 S. |
| ISBN: | 3540678271 9783540678274 0387965696 3540965696 9783642632228 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV013431412 | ||
| 003 | DE-604 | ||
| 005 | 20181009 | ||
| 007 | t | ||
| 008 | 001107s2001 gw |||| 00||| eng d | ||
| 016 | 7 | |a 960058397 |2 DE-101 | |
| 020 | |a 3540678271 |9 3-540-67827-1 | ||
| 020 | |a 9783540678274 |9 978-3-540-67827-4 | ||
| 020 | |a 0387965696 |9 0-387-96569-6 | ||
| 020 | |a 3540965696 |9 3-540-96569-6 | ||
| 020 | |a 9783642632228 |9 978-3-642-63222-8 | ||
| 035 | |a (OCoLC)248311485 | ||
| 035 | |a (DE-599)BVBBV013431412 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h fre | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-703 |a DE-355 |a DE-91G |a DE-19 |a DE-384 |a DE-11 | ||
| 050 | 0 | |a QA252.3 | |
| 082 | 0 | |a 512.55 | |
| 082 | 0 | |a 512/.55 | |
| 084 | |a SK 340 |0 (DE-625)143232: |2 rvk | ||
| 084 | |a MAT 173f |2 stub | ||
| 100 | 1 | |a Serre, Jean-Pierre |d 1926- |e Verfasser |0 (DE-588)142283126 |4 aut | |
| 240 | 1 | 0 | |a Algèbres de Lie semi-simples complexes |
| 245 | 1 | 0 | |a Complex semisimple Lie algebras |c Jean-Pierre Serre |
| 250 | |a Reprint of the 1987 ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2001 | |
| 300 | |a IX, 74 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Halbeinfache Lie-Algebra - Komplexe Zahl | |
| 650 | 0 | 7 | |a Komplexe Zahl |0 (DE-588)4128698-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lie-Algebra |0 (DE-588)4130355-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Halbeinfache Lie-Algebra |0 (DE-588)4193986-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Halbeinfache Lie-Algebra |0 (DE-588)4193986-4 |D s |
| 689 | 0 | 1 | |a Komplexe Zahl |0 (DE-588)4128698-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Lie-Algebra |0 (DE-588)4130355-6 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m SWB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009167078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009167078 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804128221853122560 |
|---|---|
| adam_text | CONTENTS CHAPTER I NILPOTENT LIE ALGEBRAS AND SOLVABLE LIE ALGEBRAS 1 1.
LOWER CENTRAL SERIES 1 2. DEFINITION OF NILPOTENT LIE ALGEBRAS 1 3. AN
EXAMPLE OF A NILPOTENT ALGEBRA 2 4. ENGEL S THEOREMS 2 5. DERIVED SERIES
3 6. DEFINITION OF SOLVABLE LIE ALGEBRAS 3 7. LIE S THEOREM 4 8.
CARTAN S CRITERION 4 CHAPTER II SEMISIMPLE LIE ALGEBRAS (GENERAL
THEOREMS) 5 1. RADICAL AND SEMISIMPLICITY 5 2. THE CARTAN-KILLING
CRITERION 6 3. DECOMPOSITION OF SEMISIMPLE LIE ALGEBRAS 6 4. DERIVATIONS
OF SEMISIMPLE LIE ALGEBRAS 7 5. SEMISIMPLE ELEMENTS AND NILPOTENT
ELEMENTS 7 6. COMPLETE REDUCIBILITY THEOREM 8 7. COMPLEX SIMPLE LIE
ALGEBRAS 8 8. THE PASSAGE FROM REAL TO COMPLEX 9 CHAPTER III CARTAN
SUBALGEBRAS 10 1. DEFINITION OF CARTAN SUBALGEBRAS 10 2. REGULAR
ELEMENTS: RANK 10 VIII CONTENTS 3. THE CARTAN SUBALGEBRA ASSOCIATED WITH
A REGULAR ELEMENT 11 4. CONJUGACY OF CARTAN SUBALGEBRAS 12 5. THE
SEMISIMPLE CASE 15 6. REAL LIE ALGEBRAS 16 CHAPTER IV THE ALGEBRA SL 2
AND ITS REPRESENTATIONS 17 1. THE LIE ALGEBRA SL 2 17 2. MODULES,
WEIGHTS, PRIMITIVE ELEMENTS 17 3. STRUCTURE OF THE SUBMODULE GENERATED
BY A PRIMITIVE ELEMENT 18 4. THE MODULES W M 19 5. STRUCTURE OF THE
FINITE-DIMENSIONAL G-MODULES 20 6. TOPOLOGICAL PROPERTIES OF THE GROUP
SL 2 21 7. APPLICATIONS 22 CHAPTER V ROOT SYSTEMS 24 1. SYMMETRIES 24 2.
DEFINITION OF ROOT SYSTEMS 25 3. FIRST EXAMPLES 26 4. THE WEYL GROUP 27
5. INVARIANT QUADRATIC FORMS 27 6. INVERSE SYSTEMS 28 7. RELATIVE
POSITION OF TWO ROOTS 29 8. BASES 30 9. SOME PROPERTIES OF BASES 31 10.
RELATIONS WITH THE WEYL GROUP 33 11. THE CARTAN MATRIX 34 12. THE
COXETER GRAPH 35 13. IRREDUCIBLE ROOT SYSTEMS 36 14. CLASSIFICATION OF
CONNECTED COXETER GRAPHS 37 15. DYNKIN DIAGRAMS 38 16. CONSTRUCTION OF
IRREDUCIBLE ROOT SYSTEMS 39 17. COMPLEX ROOT SYSTEMS 41 CHAPTER VI
STRUCTURE OF SEMISIMPLE LIE ALGEBRAS 43 1. DECOMPOSITION OF G 43 2.
PROOF OF THEOREM 2 45 3. BOREL SUBALGEBRAS 47 4. WEYL BASES 48 5.
EXISTENCE AND UNIQUENESS THEOREMS 50 6. CHEVALLEY S NORMALIZATION 51
APPENDIX. CONSTRUCTION OF SEMISIMPLE LIE ALGEBRAS BY GENERATORS AND
RELATIONS 52 CONTENTS IX CHAPTER VII LINEAR REPRESENTATIONS OF
SEMISIMPLE LIE ALGEBRAS 56 1. WEIGHTS 56 2. PRIMITIVE ELEMENTS 57 3.
IRREDUCIBLE MODULES WITH A HIGHEST WEIGHT 58 4. FINITE-DIMENSIONAL
MODULES 60 5. AN APPLICATION TO THE WEYL GROUP 62 6. EXAMPLE: SL N+1 62
7. CHARACTERS 63 8. H. WEYL S FORMULA 64 CHAPTER VIII COMPLEX GROUPS AND
COMPACT GROUPS 66 1. CARTAN SUBGROUPS 66 2. CHARACTERS 67 3. RELATIONS
WITH REPRESENTATIONS 68 4. BOREL SUBGROUPS 68 5. CONSTRUCTION OF
IRREDUCIBLE REPRESENTATIONS FROM BOREL SUBGROUPS 69 6. RELATIONS WITH
ALGEBRAIC GROUPS 70 7. RELATIONS WITH COMPACT GROUPS 70 BIBLIOGRAPHY 72
INDEX 73
|
| any_adam_object | 1 |
| author | Serre, Jean-Pierre 1926- |
| author_GND | (DE-588)142283126 |
| author_facet | Serre, Jean-Pierre 1926- |
| author_role | aut |
| author_sort | Serre, Jean-Pierre 1926- |
| author_variant | j p s jps |
| building | Verbundindex |
| bvnumber | BV013431412 |
| callnumber-first | Q - Science |
| callnumber-label | QA252 |
| callnumber-raw | QA252.3 |
| callnumber-search | QA252.3 |
| callnumber-sort | QA 3252.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 340 |
| classification_tum | MAT 173f |
| ctrlnum | (OCoLC)248311485 (DE-599)BVBBV013431412 |
| dewey-full | 512.55 512/.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 512/.55 |
| dewey-search | 512.55 512/.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Reprint of the 1987 ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02171nam a2200565 c 4500</leader><controlfield tag="001">BV013431412</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20181009 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">001107s2001 gw |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">960058397</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540678271</subfield><subfield code="9">3-540-67827-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540678274</subfield><subfield code="9">978-3-540-67827-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387965696</subfield><subfield code="9">0-387-96569-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540965696</subfield><subfield code="9">3-540-96569-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642632228</subfield><subfield code="9">978-3-642-63222-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248311485</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV013431412</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">fre</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA252.3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.55</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.55</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 340</subfield><subfield code="0">(DE-625)143232:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 173f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Serre, Jean-Pierre</subfield><subfield code="d">1926-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)142283126</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Algèbres de Lie semi-simples complexes</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Complex semisimple Lie algebras</subfield><subfield code="c">Jean-Pierre Serre</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Reprint of the 1987 ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">IX, 74 S.</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">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Springer monographs in mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Halbeinfache Lie-Algebra - Komplexe Zahl</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Komplexe Zahl</subfield><subfield code="0">(DE-588)4128698-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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">Halbeinfache Lie-Algebra</subfield><subfield code="0">(DE-588)4193986-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Halbeinfache Lie-Algebra</subfield><subfield code="0">(DE-588)4193986-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Komplexe Zahl</subfield><subfield code="0">(DE-588)4128698-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" 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="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">SWB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009167078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009167078</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></record></collection> |
| id | DE-604.BV013431412 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:45:48Z |
| institution | BVB |
| isbn | 3540678271 9783540678274 0387965696 3540965696 9783642632228 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009167078 |
| oclc_num | 248311485 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-384 DE-11 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-384 DE-11 |
| physical | IX, 74 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Serre, Jean-Pierre 1926- Verfasser (DE-588)142283126 aut Algèbres de Lie semi-simples complexes Complex semisimple Lie algebras Jean-Pierre Serre Reprint of the 1987 ed. Berlin [u.a.] Springer 2001 IX, 74 S. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Hier auch später erschienene, unveränderte Nachdrucke Halbeinfache Lie-Algebra - Komplexe Zahl Komplexe Zahl (DE-588)4128698-4 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Halbeinfache Lie-Algebra (DE-588)4193986-4 gnd rswk-swf Halbeinfache Lie-Algebra (DE-588)4193986-4 s Komplexe Zahl (DE-588)4128698-4 s DE-604 Lie-Algebra (DE-588)4130355-6 s 1\p DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009167078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Serre, Jean-Pierre 1926- Complex semisimple Lie algebras Halbeinfache Lie-Algebra - Komplexe Zahl Komplexe Zahl (DE-588)4128698-4 gnd Lie-Algebra (DE-588)4130355-6 gnd Halbeinfache Lie-Algebra (DE-588)4193986-4 gnd |
| subject_GND | (DE-588)4128698-4 (DE-588)4130355-6 (DE-588)4193986-4 |
| title | Complex semisimple Lie algebras |
| title_alt | Algèbres de Lie semi-simples complexes |
| title_auth | Complex semisimple Lie algebras |
| title_exact_search | Complex semisimple Lie algebras |
| title_full | Complex semisimple Lie algebras Jean-Pierre Serre |
| title_fullStr | Complex semisimple Lie algebras Jean-Pierre Serre |
| title_full_unstemmed | Complex semisimple Lie algebras Jean-Pierre Serre |
| title_short | Complex semisimple Lie algebras |
| title_sort | complex semisimple lie algebras |
| topic | Halbeinfache Lie-Algebra - Komplexe Zahl Komplexe Zahl (DE-588)4128698-4 gnd Lie-Algebra (DE-588)4130355-6 gnd Halbeinfache Lie-Algebra (DE-588)4193986-4 gnd |
| topic_facet | Halbeinfache Lie-Algebra - Komplexe Zahl Komplexe Zahl Lie-Algebra Halbeinfache Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009167078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT serrejeanpierre algebresdeliesemisimplescomplexes AT serrejeanpierre complexsemisimpleliealgebras |