یادداشتهای مربوط به کتابنامه ، واژه نامه و نمایه های داخل اثر
متن يادداشت
Includes bibliographical references and index.
یادداشتهای مربوط به مندرجات
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
یادداشتهای مربوط به خلاصه یا چکیده
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.
یادداشتهای مربوط به سفارشات
منبع سفارش / آدرس اشتراک
Springer
شماره انبار
978-3-7643-9997-9
ویراست دیگر از اثر در قالب دیگر رسانه
عنوان
Frobenius categories versus Brauer blocks.
شماره استاندارد بين المللي کتاب و موسيقي
376439997X
عنوان اصلی به زبان دیگر
عنوان اصلي به زبان ديگر
Grothendieck group of the Frobenius category of a Brauer block
موضوع (اسم عام یاعبارت اسمی عام)
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.
مقوله موضوعی
موضوع مستند نشده
MAT-- 014000
موضوع مستند نشده
PBG.
رده بندی ديویی
شماره
512
ويراست
22
رده بندی کنگره
شماره رده
QA251
.
5
نشانه اثر
.
P84
2009
سایر رده بندی ها
شماره رده
O187
.
2
کد سيستم
clc
نام شخص به منزله سر شناسه - (مسئولیت معنوی درجه اول )