Modular representation theory of finite groups

✍ Scribed by P Schneider

• Publisher: Springer
• Year: 2013
• Tongue: English
• Leaves: 183
• Category: Library

✦ Synopsis

1. Prerequisites in module theory -- 2. The Cartan-Brauer Triangle -- 3. The Brauer character -- 4. Green's theory of indecomposable modules -- 5. Blocks

✦ Table of Contents

Cover......Page 1
Modular Representation Theory of Finite Groups......Page 3
Preface......Page 5
Contents......Page 7
1.1 Chain Conditions and More......Page 9
1.2 Radicals......Page 11
1.3 I-Adic Completeness......Page 12
1.4 Unique Decomposition......Page 17
1.5 Idempotents and Blocks......Page 23
1.6 Projective Modules......Page 34
1.7 Grothendieck Groups......Page 42
2.1 The Setting......Page 50
2.2 The Triangle......Page 53
2.3 The Ring Structure of RF (G), and Induction......Page 61
2.4 The Burnside Ring......Page 66
2.5 Clifford Theory......Page 74
2.6 Brauer's Induction Theorem......Page 78
2.7 Splitting Fields......Page 82
2.8 Properties of the Cartan-Brauer Triangle......Page 85
3.1 Definitions......Page 94
3.2 Properties......Page 98
4.1 Relatively Projective Modules......Page 104
4.2 Vertices and Sources......Page 112
4.3 The Green Correspondence......Page 117
4.4 An Example: The Group SL2 (Fp)......Page 126
4.5 Green's Indecomposability Theorem......Page 147
5.1 Blocks and Simple Modules......Page 154
5.2 Central Characters......Page 158
5.3 Defect Groups......Page 160
5.4 The Brauer Correspondence......Page 166
5.5 Brauer Homomorphisms......Page 172
References......Page 181
Index......Page 182