Lluís Puig

Frobenius Categories versus Brauer Blocks (eBook, PDF)

The Grothendieck Group of the Frobenius Category of a Brauer Block

• Format: PDF

Produktdetails

• Verlag: Springer Basel
• Erscheinungstermin: 22. Juni 2009
• Englisch
• ISBN-13: 9783764399986
• Artikelnr.: 37397704

Inhaltsangabe

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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.

Rezensionen

From the reviews:

"The concept of Frobenius category (also called saturated fusion system) has been developed by Lluis Puig many years ago. ... This volume is a research monograph containing many original results which appear for the first time in print ... . The book ends with Appendix developing the author's point of view on cohomology of small categories. ... the book is a necessary tool for any researcher in the field." (Andrei Marcus, Studia Universitatis Babes-Bolyai, Mathematica, Vol. LV (4), December, 2010)

"In recent years a new concept-called Frobenius category by Puig and fusion system by others-has become very successful in the representation theory of finite groups. ... the book gives an account of the early developments and definitions presented by Puig, as they were given in his first manuscripts. This certainly is of great importance because it makes the first, original definitions of Puig accessible to a wide audience." (Alexander Zimmermann, Mathematical Reviews, Issue 2010 j)