Lie algebras of finite and affine type:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
2005
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
96 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 632 S. |
| ISBN: | 0521851386 9780521851381 |
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Record in the Search Index
| _version_ | 1804133560207015936 |
|---|---|
| adam_text | LIE ALGEBRAS OF FINITE AND AFFINE TYPE R. W. CARTER MATHEMATICS
INSTITUTE UNIVERSITY OF WARWICK CAMBRIDGE UNIVERSITY PRESS CONTENTS
PREFACE PAGE XIII BASIC CONCEPTS 1 1.1 ELEMENTARY PROPERTIES OF LIE
ALGEBRAS 1 1.2 REPRESENTATIONS AND MODULES 5 1.3 ABELIAN, NILPOTENT AND
SOLUBLE LIE ALGEBRAS 7 REPRESENTATIONS OF SOLUBLE AND NILPOTENT LIE
ALGEBRAS 11 2.1 REPRESENTATIONS OF SOLUBLE LIE ALGEBRAS 11 2.2
REPRESENTATIONS OF NILPOTENT LIE ALGEBRAS 14 CARTAN SUBALGEBRAS 23 3.1
EXISTENCE OF CARTAN SUBALGEBRAS 23 3.2 DERIVATIONS AND AUTOMORPHISMS 25
3.3 IDEAS FROM ALGEBRAIC GEOMETRY 27 3.4 CONJUGACY OF CARTAN SUBALGEBRAS
33 THE CARTAN DECOMPOSITION 36 4.1 SOME PROPERTIES OF ROOT SPACES 36 4.2
THE KILLING FORM 39 4.3 THE CARTAN DECOMPOSITION OF A SEMISIMPLE LIE
ALGEBRA 45 4.4 THE LIE ALGEBRA §I N (C) 52 THE ROOT SYSTEM AND THE WEYL
GROUP 56 5.1 POSITIVE SYSTEMS AND FUNDAMENTAL SYSTEMS OF ROOTS 56 5.2
THE WEYL GROUP 59 5.3 GENERATORS AND RELATIONS FOR THE WEYL GROUP 65 .
VN VIII CONTENTS 6 THE CARTAN MATRIX AND THE DYNKIN DIAGRAM 69 6.1 THE
CARTAN MATRIX 69 6.2 THE DYNKIN DIAGRAM 72 6.3 CLASSIFICATION OF DYNKIN
DIAGRAMS 74 6.4 CLASSIFICATION OF CARTAN MATRICES 80 7 THE EXISTENCE AND
UNIQUENESS THEOREMS 88 7.1 SOME PROPERTIES OF STRUCTURE CONSTANTS 88 7.2
THE UNIQUENESS THEOREM 93 7.3 SOME GENERATORS AND RELATIONS IN A SIMPLE
LIE ALGEBRA 96 7.4 THE LIE ALGEBRAS L(A) AND L(A) 98 7.5 THE EXISTENCE
THEOREM 105 8 THE SIMPLE LIE ALGEBRAS 121 8.1 LIE ALGEBRAS OF TYPE A,
122 8.2 LIE ALGEBRAS OF TYPE D, 124 8.3 LIE ALGEBRAS OF TYPE B, 128 8.4
LIE ALGEBRAS OF TYPE C, 132 8.5 LIE ALGEBRAS OF TYPE G 2 135 8.6 LIE
ALGEBRAS OF TYPE F 4 138 8.7 LIE ALGEBRAS OF TYPES E B , E 7 , 8 140
8.8 PROPERTIES OF LONG AND SHORT ROOTS 145 9 SOME UNIVERSAL
CONSTRUCTIONS 152 9.1 THE UNIVERSAL ENVELOPING ALGEBRA 152 9.2 THE
POINCARE-BIRKHOFF-WITT BASIS THEOREM 155 9.3 FREE LIE ALGEBRAS 160 9.4
LIE ALGEBRAS DEFINED BY GENERATORS AND RELATIONS 163 9.5 GRAPH
AUTOMORPHISMS OF SIMPLE LIE ALGEBRAS 165 10 IRREDUCIBLE MODULES FOR
SEMISIMPLE LIE ALGEBRAS 176 10.1 VERMA MODULES 176 10.2 FINITE
DIMENSIONAL IRREDUCIBLE MODULES 186 10.3 THE FINITE DIMENSIONALITY
CRITERION 190 11 FURTHER PROPERTIES OF THE UNIVERSAL ENVELOPING ALGEBRA
201 11.1 RELATIONS BETWEEN THE ENVELOPING ALGEBRA AND THE SYMMETRIC
ALGEBRA 201 11.2 INVARIANT POLYNOMIAL FUNCTIONS 207 11.3 THE STRUCTURE
OF THE RING OF POLYNOMIAL INVARIANTS 216 11.4 THE KILLING ISOMORPHISMS
222 CONTENTS IX 11.5 THE CENTRE OF THE ENVELOPING ALGEBRA 226 11.6 THE
CASIMIR ELEMENT 238 12 CHARACTER AND DIMENSION FORMULAE 241 12.1
CHARACTERS OF L-MODULES 241 12.2 CHARACTERS OF VERMA MODULES 244 12.3
CHAMBERS AND ROOTS 246 12.4 COMPOSITION FACTORS OF VERMA MODULES 255
12.5 WEYL S CHARACTER FORMULA 258 12.6 COMPLETE REDUCIBILITY 262 13
FUNDAMENTAL MODULES FOR SIMPLE LIE ALGEBRAS 267 13.1 AN ALTERNATIVE FORM
OF WEYL S DIMENSION FORMULA 267 13.2 FUNDAMENTAL MODULES FOR A, 268 13.3
EXTERIOR POWERS OF MODULES 270 13.4 FUNDAMENTAL MODULES FOR B, AND D,
21A 13.5 CLIFFORD ALGEBRAS AND SPIN MODULES 281 13.6 FUNDAMENTAL MODULES
FOR C, 292 13.7 CONTRACTION MAPS 295 13.8 FUNDAMENTAL MODULES FOR
EXCEPTIONAL ALGEBRAS 303 14 GENERALISED CARTAN MATRICES AND KAC-MOODY
ALGEBRAS 319 14.1 REALISATIONS OF A SQUARE MATRIX 319 14.2 THE LIE
ALGEBRA L{A) ASSOCIATED WITH A COMPLEX MATRIX 322 14.3 THE KAC-MOODY
ALGEBRA L(A) 331 15 THE CLASSIFICATION OF GENERALISED CARTAN MATRICES
336 15.1 A TRICHOTOMY FOR INDECOMPOSABLE GCMS 336 15.2 SYMMETRISABLE
GENERALISED CARTAN MATRICES 344 15.3 THE CLASSIFICATION OF AFFINE
GENERALISED CARTAN MATRICES 351 16 THE INVARIANT FORM, WEYL GROUP AND
ROOT SYSTEM 360 16.1 THE INVARIANT BILINEAR FORM 360 16.2 THE WEYL GROUP
OF A KAC-MOODY ALGEBRA 371 16.3 THE ROOTS OF A KAC-MOODY ALGEBRA 377 X
CONTENTS 17 KAC-MOODY ALGEBRAS OF AFFINE TYPE 386 17.1 PROPERTIES OF THE
AFFINE CARTAN MATRIX 386 17.2 THE ROOTS OF AN AFFINE KAC-MOODY ALGEBRA
394 17.3 THE WEYL GROUP OF AN AFFINE KAC-MOODY ALGEBRA 404 18
REALISATIONS OF AFFINE KAC-MOODY ALGEBRAS 416 18.1 LOOP ALGEBRAS AND
CENTRAL EXTENSIONS 416 18.2 REALISATIONS OF UNTWISTED AFFINE KAC-MOODY
ALGEBRAS 421 18.3 SOME GRAPH AUTOMORPHISMS OF AFFINE ALGEBRAS 426 18.4
REALISATIONS OF TWISTED AFFINE ALGEBRAS 429 19 SOME REPRESENTATIONS OF
SYMMETRISABLE KAC-MOODY ALGEBRAS 452 19.1 THE CATEGORY 0 OF L(A)-MODULES
452 19.2 THE GENERALISED CASIMIR OPERATOR 459 19.3 KAC CHARACTER FORMULA
466 19.4 GENERATORS AND RELATIONS FOR SYMMETRISABLE ALGEBRAS 474 20
REPRESENTATIONS OF AFFINE KAC-MOODY ALGEBRAS 484 20.1 MACDONALD S
IDENTITIES 484 20.2 SPECIALISATIONS OF MACDONALD S IDENTITIES 491 20.3
IRREDUCIBLE MODULES FOR AFFINE ALGEBRAS 494 20.4 THE FUNDAMENTAL MODULES
FOR L(A T ) 504 20.5 THE BASIC REPRESENTATION 508 21 BORCHERDS LIE
ALGEBRAS 519 21.1 DEFINITION AND EXAMPLES OF BORCHERDS ALGEBRAS 519 21.2
REPRESENTATIONS OF BORCHERDS ALGEBRAS 524 21.3 THE MONSTER LIE ALGEBRA
530 APPENDIX 540 SUMMARY PAGES - EXPLANATION 540 TYPE A, 543 TYPE B, 545
TYPE C, 547 TYPE D, 549 TYPE 6 551 TYPE E 7 553 TYPE E S 555 TYPE F 4
557 TYPE G 2 559
|
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| author | Carter, Roger W. 1934- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.482 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV020006502 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:10:39Z |
| institution | BVB |
| isbn | 0521851386 9780521851381 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013328139 |
| oclc_num | 254139739 |
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| physical | XVII, 632 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Carter, Roger W. 1934- Verfasser (DE-588)128642831 aut Lie algebras of finite and affine type R. W. Carter 1. publ. Cambridge u.a. Cambridge Univ. Pr. 2005 XVII, 632 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 96 Kac-Moody-Algebra Lie algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Kac-Moody-Algebra (DE-588)4223399-9 s DE-604 Lie-Algebra (DE-588)4130355-6 s Cambridge studies in advanced mathematics 96 (DE-604)BV000003678 96 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013328139&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carter, Roger W. 1934- Lie algebras of finite and affine type Cambridge studies in advanced mathematics Kac-Moody-Algebra Lie algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4223399-9 (DE-588)4130355-6 |
| title | Lie algebras of finite and affine type |
| title_auth | Lie algebras of finite and affine type |
| title_exact_search | Lie algebras of finite and affine type |
| title_full | Lie algebras of finite and affine type R. W. Carter |
| title_fullStr | Lie algebras of finite and affine type R. W. Carter |
| title_full_unstemmed | Lie algebras of finite and affine type R. W. Carter |
| title_short | Lie algebras of finite and affine type |
| title_sort | lie algebras of finite and affine type |
| topic | Kac-Moody-Algebra Lie algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Kac-Moody-Algebra Lie algebras Lie-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013328139&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT carterrogerw liealgebrasoffiniteandaffinetype |