Lie algebras with triangular decompositions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1995
|
| Series: | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts
[11] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 685 S. graph. Darst. |
| ISBN: | 0471633046 |
Staff View
MARC
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| 264 | 1 | |a New York [u.a.] |b Wiley |c 1995 | |
| 300 | |a XX, 685 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804124733876207616 |
|---|---|
| adam_text | Contents
Introduction xi
How to Read This Book xv
Course Outlines xix
Chapter 1 Lie Algebras 1
1.1 Basic Definitions
1.2 Tensor, Symmetric, and Exterior Algebras 9
1.3 Gradings 15
1.4 Virasoro and Heisenberg Algebras 20
1.5 Derivations 23
1.6 Representations 28
1.7 Invariant Bilinear Forms 35
1.8 Universal Enveloping Algebras 38
1.9 Central Extensions 49
1.10 Free Lie Algebras 59
1.11 The Campbell Baker Hausdorff Formula 65
1.12 Extensions of Modules 71
Exercises 80
Chapter 2 Lie Algebras Admitting Triangular Decompositions 90
2.1 Triangular and Weight Space Decompositions 91
2.2 Highest Weight Modules 103
2.3 Verma Modules 106
2.4 3I2(K) Theorem 116
2.5 Characters 128
2.6 The Category 141
2.7 The Radical 160
2.8 The Shapovalov form 168
2.9 Jantzen Filtrations 175
2.10 Bernstein Gel fand Gel fand Duality 184
2.11 Embeddings of Verma Modules 200
2.12 Decomposition of Modules in Category 204
Exercises 209
vii
viii Contents
Chapter 3 Lattices and Root Systems 216
3.1 Lattices 217
3.2 Finite Root Systems 229
3.3 Bases for Finite Root Systems 239
3.4 Graphs and Coxeter Dynkin Diagrams 247
3.5 Classification of Cartan Matrices and Finite Root Systems 258
3.6 The Perron Frobenius Theorem and Its Consequences 272
3.7 Constructing Lie Algebras from Lattices 280
3.8 Central Extensions of Lattices 289
Exercises 302
Chapter 4 Contragredient Lie Algebras 309
4.1 Contragredient Lie algebras 310
4.2 Realizations of Contragredient Lie Algebras 330
4.3 Embeddings, Field Extensions, and Decomposability 342
4.4 Invariant Bilinear Forms 355
4.5 Casimir Kac Operators 367
4.6 The Radical Theorem 375
4.7 Hermitian Contragredient Forms 382
Exercises 385
Chapter 5 The Weyl Group and Its Geometry 395
5.1 Root Data 396
5.2 The Length Function 408
5.3 Coxeter Groups and the Exchange Condition 418
5.4 The Bruhat Ordering 425
5.5 Morphisms of Root Data: Subroot Systems 430
5.6 The Geometry of a Set of Root Data 436
5.7 Subroot Systems 457
5.8 Imaginary Roots 464
5.9 Conjugacy of Bases 472
Exercises 476
Chapter 6 Category 0 for Kac Moody Algebras 483
6.1 Integrable Modules 484
6.2 Weight Systems 508
6.3 The Triangular Decomposition of G 516
6.4 The Formulas of Weyl Macdonald Kac 531
6.5 Complete Reducibility 542
6.6 ShapOvalov Determinant Formula for Kac Moody Algebras 545
6.7 The BGG Theorem and Generalization 556
Contents ix
6.8 Translation Functors and the Generalized
Character Formula 564
Exercises 574
Chapter 7 Conjugacy Theorems 586
7.1 Locally Finite Endomorphisms and Jordan Chevalley
Decompositions 586
7.2 Locally Finite Elements in Kac Moody Algebras 606
7.3 The Kostant Cone 612
7.4 Conjugacy of Split Cartan Subalgebras 623
Exercises 639
Appendix ^ An Extended Example 647
Bibliography 675
Index 681
|
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| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV010315155 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:22Z |
| institution | BVB |
| isbn | 0471633046 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006863465 |
| oclc_num | 27226618 |
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| physical | XX, 685 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Wiley |
| record_format | marc |
| series | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts |
| series2 | Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts A Wiley-Interscience publication |
| spelling | Moody, Robert V. 1941- Verfasser (DE-588)172277922 aut Lie algebras with triangular decompositions Robert V. Moody ; Arturo Pianzola New York [u.a.] Wiley 1995 XX, 685 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts [11] A Wiley-Interscience publication Décomposition (Mathématiques) ram Lie, algèbres de ram Lie-algebra's gtt Ontleding (wiskunde) gtt Decomposition (Mathematics) Lie algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd rswk-swf Kac-Moody-Algebra (DE-588)4223399-9 s DE-604 Pianzola, Arturo Verfasser aut Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts [11] (DE-604)BV012067942 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006863465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moody, Robert V. 1941- Pianzola, Arturo Lie algebras with triangular decompositions Canadian Mathematical Society: Canadian Mathematical Society series of monographs and advanced texts Décomposition (Mathématiques) ram Lie, algèbres de ram Lie-algebra's gtt Ontleding (wiskunde) gtt Decomposition (Mathematics) Lie algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd |
| subject_GND | (DE-588)4223399-9 |
| title | Lie algebras with triangular decompositions |
| title_auth | Lie algebras with triangular decompositions |
| title_exact_search | Lie algebras with triangular decompositions |
| title_full | Lie algebras with triangular decompositions Robert V. Moody ; Arturo Pianzola |
| title_fullStr | Lie algebras with triangular decompositions Robert V. Moody ; Arturo Pianzola |
| title_full_unstemmed | Lie algebras with triangular decompositions Robert V. Moody ; Arturo Pianzola |
| title_short | Lie algebras with triangular decompositions |
| title_sort | lie algebras with triangular decompositions |
| topic | Décomposition (Mathématiques) ram Lie, algèbres de ram Lie-algebra's gtt Ontleding (wiskunde) gtt Decomposition (Mathematics) Lie algebras Kac-Moody-Algebra (DE-588)4223399-9 gnd |
| topic_facet | Décomposition (Mathématiques) Lie, algèbres de Lie-algebra's Ontleding (wiskunde) Decomposition (Mathematics) Lie algebras Kac-Moody-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006863465&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012067942 |
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