Projective representations of finite groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1985
|
| Series: | Pure and applied mathematics
94 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 604 - 627 |
| Physical Description: | XIII, 644 S. graph. Darst. |
| ISBN: | 0824773136 |
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MARC
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| 245 | 1 | 0 | |a Projective representations of finite groups |c Gregory Karpilovsky |
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Record in the Search Index
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| adam_text | Contents
PREFACE v
CHAPTER 1. PRELIMINARIES 1
1. Notation, Terminology, and Background
Information 1
2. Semisimple Algebras 18
3. Extension of Ground Fields 21
4. Separable Modules and Algebras 24
5. Absolutely Irreducible and Absolutely
Indecomposable Modules 26
6. Splitting Fields 27
CHAPTER 2. PREREQUISITES IN COHOMOLOGY THEORY 31
1. Second Cohomology Group and Central
Group Extensions 31
2. Some Cohomology Sequences 38
3. Basic Properties of Cohomology Groups 52
CHAPTER 3. PROJECTIVE REPRESENTATIONS: FOUNDATIONS
OF THE THEORY 70
1. Definitions 70
2. Twisted Group Algebras 76
3. Representation Groups: Existence and
Characterizations 91
4. An Upper Bound for the Number of
Nonisomorphic Representation Groups 99
5. Representation Groups of Abelian Groups 104
6. The Number of Irreducible FaG Modules 107
7. Projective Representations of Particular
Groups 118
CHAPTER 4. THE SCHUR MULTIPLIER 132
1. Preliminary Results 132
2. A Fundamental Theorem and Its Applications 139
xi
xii Contents
3. Perfect Groups 149
4. Central Quotients 154
5. Wreath Products 159
6. Metacyclic Groups 167
7. Extra Special p Groups 172
8. Symmetric and Alternating Groups 176
9. Special Linear Groups 187
CHAPTER 5. INDUCED REPRESENTATIONS 19 3
1. Tensor Products of Representations 19 3
2. Induction and Imprimitivity 199
3. Formal Properties of Induced Modules 202
4. Annihilators of Induced Modules 211
5. Induction, Restriction, and Outer
Tensor Products 217
6. Nakayama Reciprocity 221
7. Mackey s Theorems 224
8. Relative Projective and Injective
Modules over Twisted Group Algebras 239
9. Vertices and Sources 253
10. The Green Correspondence 261
CHAPTER 6. CLIFFORD THEORY 267
1. The Restriction of Irreducible Modules
to Normal Subgroups 267
2. Extendibility and Obstruction Cocycles 271
3. Inflated Modules 282
4. G Invariant Constituents 291
5. Applications 296
6. Decomposition of Induced Modules from
Normal Subgroups 311
7. Restriction, Induction, and Extendibility
of Indecomposable Modules 317
8. Further Application: Dimensions of
Projective Covers 335
CHAPTER 7. PROJECTIVE CHARACTERS 350
1. Introduction 350
2. Class Function Cocycles 362
3. Orthogonality Relations 367
4. Induced Characters 374
5. Characterization of a Characters 382
6. Rational and Real Valued ex Characters 389
7. An Analog of Artin s Induction Theorem
for Rational a Characters 39 3
8. Character Theoretic Implications of
Clifford Theory 39 8
9. Berman Reynolds Permutation Lemma and
Its Applications 404
Contents xiii
CHAPTER 8. THE SCHUR INDEX 413
1. Behavior of Irreducible Modules Under
Extension of Ground Field 414
2. The Schur Index of Representations of
Algebras 4 29
3. Projective Schur Index 438
CHAPTER 9. BLOCK THEORY FOR TWISTED GROUP ALGEBRAS 445
1. Direct Decompositions of Algebras 446
2. Block Idempotents of Twisted Group
Algebras 456
3. The Conlon Reynolds Correspondence 462
4. Behavior of Defect Groups of Blocks
Under Extension of Ground Field 469
5. Blocks and Normal Subgroups 473
6. Blocks with Normal Defect Groups 484
7. Reduction to Blocks of Defect Zero 487
8. The Number of Blocks of a Given Defect 499
9. The Cartan Matrix 505
10. Blocks of p Nilpotent Groups 511
1
11. Fa Xa(G x G) Modules 517
12. Relations Between the Green and
Conlon Reynolds Correspondences 525
13. Blocks of Representation Groups 533
14. Blocks and Vertices 539
15. The Jacobson Radical of a Block 545
16. Blocks with Central Defect Groups 553
CHAPTER 10. MISCELLANEOUS 562
1. Dimensions of Indecomposable F G Modules 562
2. Counting Irreducible a Representations
over Arbitrary Fields 564
3. Schur Multiplier of Cyclic Extensions 572
4. Faithful Irreducible Representations 577
5. Socle and Commutator Subspace of
Symmetric Algebras 591
6. Blocks with a Unique Isomorphism Class
of Irreducible Modules 598
BIBLIOGRAPHY 604
NOTATION 629
INDEX 635
|
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| id | DE-604.BV002295779 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:43:34Z |
| institution | BVB |
| isbn | 0824773136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001508765 |
| oclc_num | 246624839 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-703 DE-824 DE-29T DE-19 DE-BY-UBM DE-11 DE-706 |
| physical | XIII, 644 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Karpilovsky, Gregory Verfasser aut Projective representations of finite groups Gregory Karpilovsky New York [u.a.] Dekker 1985 XIII, 644 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 94 Literaturverz. S. 604 - 627 Projektive Darstellung (DE-588)4382502-3 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Projektive Darstellung (DE-588)4382502-3 s DE-604 Pure and applied mathematics 94 (DE-604)BV000001885 94 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001508765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karpilovsky, Gregory Projective representations of finite groups Pure and applied mathematics Projektive Darstellung (DE-588)4382502-3 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4382502-3 (DE-588)4014651-0 |
| title | Projective representations of finite groups |
| title_auth | Projective representations of finite groups |
| title_exact_search | Projective representations of finite groups |
| title_full | Projective representations of finite groups Gregory Karpilovsky |
| title_fullStr | Projective representations of finite groups Gregory Karpilovsky |
| title_full_unstemmed | Projective representations of finite groups Gregory Karpilovsky |
| title_short | Projective representations of finite groups |
| title_sort | projective representations of finite groups |
| topic | Projektive Darstellung (DE-588)4382502-3 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Projektive Darstellung Endliche Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001508765&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT karpilovskygregory projectiverepresentationsoffinitegroups |