عنوان

Frobenius categories versus Brauer blocks :

(Number (ISBN

3764399988

(Number (ISBN

9783764399986

Erroneous ISBN

376439997X

Erroneous ISBN

9783764399979

Number

b773050

Title Proper

Frobenius categories versus Brauer blocks :

General Material Designation

[Book]

Other Title Information

the Grothendieck group of the Frobenius category of a Brauer block /

First Statement of Responsibility

Lluís Puig.

Place of Publication, Distribution, etc.

Boston, Mass. :

Name of Publisher, Distributor, etc.

Birkhäuser,

Date of Publication, Distribution, etc.

©2009.

Specific Material Designation and Extent of Item

1 online resource (498 pages)

Series Title

Progress in mathematics ;

Volume Designation

274

Text of Note

Includes bibliographical references and index.

Text of Note

Introduction -- 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.

0

Text of Note

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 abstract setting of the Frobenius categories -- also called the Saturated fusion systems in the literature -- created by the author fifteen years ago for a better understanding of what was loosely called the local theory of a finite group around a prime number p or, later, around a Brauer block, and for the purpose of an eventual classification -- a reasonable concept of simple Frobenius category arises. On the other hand, the book develops this abstract setting in parallel with its application to the Brauer blocks, giving the detailed translation of any abstract concept in the particular context of the blocks. One of the new features in this direction is a framework for a deeper understanding of one of the central open problems in modular representation theory, known as Alperin's Weight Conjecture (AWC). Actually, this new framework suggests a more general form of AWC, and a significant result of the book is a reduction theorem of this form of AWC to quasi-simple groups. Although this book is a research monograph, all the arguments are widely developed to make it accessible to the interested graduate students and, at the same time, to put them on the verge of the research on this new subject: the third part of the book on the localities associated to a Frobenius category gives some insight on the open question about the existence and the uniquenes of a perfect locality -- also called centric linking system in the literature. We have developed a long introduction to explain our purpose and to provide a guideline for the reader throughout the twenty four sections. A systematic appendix on the cohomology of categories completes the book.

Source for Acquisition/Subscription Address

Springer

Stock Number

978-3-7643-9997-9

Title

Frobenius categories versus Brauer blocks.

International Standard Book Number

376439997X

Parallel Title

Grothendieck group of the Frobenius category of a Brauer block

Brauer groups.

Finite groups.

Frobenius algebras.

Frobenius groups.

Grothendieck groups.

Representations of groups.

Brauer groups.

Brauer groups.

Darstellungstheorie-- Endliche Gruppe.

Endliche Gruppe-- Darstellungstheorie.

Finite groups.

Finite groups.

Frobenius algebras.

Frobenius algebras.

Frobenius groups.

Frobenius groups.

Grothendieck groups.

Grothendieck groups.

MATHEMATICS-- Group Theory.

Representations of groups.

Representations of groups.

MAT-- 014000

PBG.

Number

Edition

Class number

Book number

Class number

System Code

Puig, Luis.

Date of Transaction

20201203043453.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y