Frobenius Categories versus Brauer Blocks (eBook)

Contents 6
Introduction 7
Chapter 1 20
General notation and quoted results 20
Chapter 2 Frobenius P-categories: the .rst de.nition 31
Chapter 3 The Frobenius P-category ofa block 42
Chapter 4 Nilcentralized, selfcentralizing and intersected objects in Frobenius P-categories 49
Chapter 5 Alperin fusions in Frobenius P-categories 58
Chapter 6 Exterior quotient ofa Frobenius P-category over the selfcentralizing objects 73
Chapter 7 Nilcentralized and selfcentralizing Brauer pairs in blocks 92
Chapter 8 Decompositions for Dade P-algebras 102
Chapter 9 Polarizations for Dade P-algebras 115
Chapter 10 A gluing theorem for Dade P-algebras 134
Chapter 11 The nilcentralized chain k*- function of a block 147
Chapter 12 Quotients and normal subcategories in Frobenius P-categories 174
Chapter 13 The hyperfocal subcategory ofa Frobenius P-category 189
Chapter 14 The Grothendieck groups of a Frobenius P-category 204
Chapter 15 Reduction results for Grothendieck groups 233
Chapter 16 The local-global question: reduction to the simple groups 278
Chapter 17 Localities associated with a Frobenius P-category 310
Chapter 18 The localizers in a Frobenius P-category 323
Chapter 19 Solvability for Frobenius P-categories 350
Chapter 20 A perfect F-locality from a perfect Fsc -locality 357
Chapter 21 Frobenius P-categories: the second definition 376
Chapter 22 The basic F-locality 384
Chapter 23 Narrowing the basic F sc-locality 395
Chapter 24 Looking for a perfect Fsc -locality 422
Appendix Simpliciality 433
References 472
Index 476