عنوان

Frobenius categories versus Brauer blocks :

شابک

3764399988

شابک

9783764399986

شابک اشتباه

376439997X

شابک اشتباه

9783764399979

شماره

b773050

عنوان اصلي

Frobenius categories versus Brauer blocks :

نام عام مواد

[Book]

ساير اطلاعات عنواني

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

نام نخستين پديدآور

Lluís Puig.

محل نشرو پخش و غیره

Boston, Mass. :

نام ناشر، پخش کننده و غيره

Birkhäuser,

تاریخ نشرو بخش و غیره

©2009.

نام خاص و کميت اثر

1 online resource (498 pages)

عنوان فروست

Progress in mathematics ;

مشخصه جلد

274

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.

منبع سفارش / آدرس اشتراک

Springer

شماره انبار

978-3-7643-9997-9

عنوان

Frobenius categories versus Brauer blocks.

شماره استاندارد بين المللي کتاب و موسيقي

376439997X

عنوان اصلي به زبان ديگر

Grothendieck group of the Frobenius category of a Brauer block

موضوع مستند نشده

Brauer groups.

موضوع مستند نشده

Finite groups.

موضوع مستند نشده

Frobenius algebras.

موضوع مستند نشده

Frobenius groups.

موضوع مستند نشده

Grothendieck groups.

موضوع مستند نشده

Representations of groups.

موضوع مستند نشده

Brauer groups.

موضوع مستند نشده

Brauer groups.

موضوع مستند نشده

Darstellungstheorie-- Endliche Gruppe.

موضوع مستند نشده

Endliche Gruppe-- Darstellungstheorie.

موضوع مستند نشده

Finite groups.

موضوع مستند نشده

Finite groups.

موضوع مستند نشده

Frobenius algebras.

موضوع مستند نشده

Frobenius algebras.

موضوع مستند نشده

Frobenius groups.

موضوع مستند نشده

Frobenius groups.

موضوع مستند نشده

Grothendieck groups.

موضوع مستند نشده

Grothendieck groups.

موضوع مستند نشده

MATHEMATICS-- Group Theory.

موضوع مستند نشده

Representations of groups.

موضوع مستند نشده

Representations of groups.

موضوع مستند نشده

MAT-- 014000

موضوع مستند نشده

PBG.

شماره

ويراست

شماره رده

نشانه اثر

شماره رده

کد سيستم

مستند نام اشخاص تاييد نشده

Puig, Luis.

تاريخ عمليات

20201203043453.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y