Volume 274 2009

Frobenius Categories versus Brauer Blocks

The Grothendieck Group of the Frobenius Category of a Brauer Block

Authors:

ISBN: 978-3-7643-9997-9 (Print) 978-3-7643-9998-6 (Online)

Table of contents (25 chapters)

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  1. Front Matter

    Pages i-v

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    Book Chapter

    Pages 1-13

    Introduction

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    Book Chapter

    Pages 15-25

    General notation and quoted results

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    Book Chapter

    Pages 27-37

    Frobenius P-categories: the first definition

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    Book Chapter

    Pages 39-45

    The Frobenius P-category of a block

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    Pages 47-55

    Nilcentralized, selfcentralizing and intersected objects in Frobenius P-categories

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    Book Chapter

    Pages 57-71

    Alperin fusions in Frobenius P-categories

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    Book Chapter

    Pages 73-91

    Exterior quotient of a Frobenius P-category over the selfcentralizing objects

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    Book Chapter

    Pages 93-102

    Nilcentralized and selfcentralizing Brauer pairs in blocks

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    Book Chapter

    Pages 103-115

    Decompositions for Dade P-algebras

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    Pages 117-135

    Polarizations for Dade P-algebras

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    Book Chapter

    Pages 137-149

    A gluing theorem for Dade P-algebras

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    Book Chapter

    Pages 151-177

    The nilcentralized chain k *-functor of a block

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    Book Chapter

    Pages 179-193

    Quotients and normal subcategories in Frobenius P-categories

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    Book Chapter

    Pages 195-209

    The hyperfocal subcategory of a Frobenius P-category

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    Book Chapter

    Pages 211-239

    The Grothendieck groups of a Frobenius P-category

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    Book Chapter

    Pages 241-285

    Reduction results for Grothendieck groups

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    Book Chapter

    Pages 287-318

    The local-global question: reduction to the simple groups

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    Book Chapter

    Pages 319-331

    Localities associated with a Frobenius P-category

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    Book Chapter

    Pages 333-359

    The localizers in a Frobenius P-category

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    Book Chapter

    Pages 361-367

    Solvability for Frobenius P-categories

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