Frobenius Categories versus Brauer Blocks The Grothendieck Group of the Frobenius Category of a Brauer Block /

• Main Author: Puig, Lluís (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2009.
• Series: Progress in Mathematics ; 274
• Subjects: Mathematics.; Group theory.; Algebraic topology.; Group Theory and Generalizations.; Algebraic Topology.

This book contributes to important questions in the representation theory of finite groups over fields of positive characteristic — an area of research initiated by Richard Brauer sixty years ago with the introduction of the blocks of characters. On the one hand, it introduces and develops the abstr...

Table of Contents:

• General notation and quoted results
• Frobenius P-categories: the first definition
• The Frobenius P-category of a block
• Nilcentralized, selfcentralizing and intersected objects in Frobenius P-categories
• Alperin fusions in Frobenius P-categories
• Exterior quotient of a Frobenius P-category over the selfcentralizing objects
• Nilcentralized and selfcentralizing Brauer pairs in blocks
• Decompositions for Dade P-algebras
• Polarizations for Dade P-algebras
• A gluing theorem for Dade P-algebras
• The nilcentralized chain k*-functor of a block
• Quotients and normal subcategories in Frobenius P-categories
• The hyperfocal subcategory of a Frobenius P-category
• The Grothendieck groups of a Frobenius P-category
• Reduction results for Grothendieck groups
• The local-global question: reduction to the simple groups
• Localities associated with a Frobenius P-category
• The localizers in a Frobenius P-category
• Solvability for Frobenius P-categories
• A perfect F-locality from a perfect Fsc -locality
• Frobenius P-categories: the second definition
• The basic F-locality
• Narrowing the basic Fsc-locality
• Looking for a perfect Fsc-locality.