Puig Frobenius Categories versus Brauer Blocks

The Grothendieck Group of the Frobenius Category of a Brauer Block
2009
ISBN: 978-3-7643-9998-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 274, 498 Seiten, eBook

Reihe: Progress in Mathematics

This book contributes to important questions in modern representation theory of finite groups. It introduces and develops the abstract setting of the Frobenius categories and gives the application of the abstract setting to the blocks.

Zielgruppe

Research

Autoren/Hrsg.

Puig, Lluís

Inhaltsverzeichnis

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.