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Titlebook: Representation Theory of Finite Groups: a Guidebook; David A. Craven Textbook 2019 Springer Nature Switzerland AG 2019 Group representatio

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书目名称Representation Theory of Finite Groups: a Guidebook
编辑David A. Craven
视频video
概述Provides an overview of the whole subject of representation theory of finite groups.A unique survey of current research aimed at beginning researchers.Only basic knowledge is assumed with most topics
丛书名称Universitext
图书封面Titlebook: Representation Theory of Finite Groups: a Guidebook;  David A. Craven Textbook 2019 Springer Nature Switzerland AG 2019 Group representatio
描述.This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures...The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups...Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars..
出版日期Textbook 2019
关键词Group representation; Representations of finite groups; Representations of symmetric groups; Finite gro
版次1
doihttps://doi.org/10.1007/978-3-030-21792-1
isbn_softcover978-3-030-21791-4
isbn_ebook978-3-030-21792-1Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Nature Switzerland AG 2019
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The Basics,stly to fix notation. We do the module theory first, seeing .-modules and their basic properties. Then we proceed onto character theory, and see the contents of a typical undergraduate course at a U.K. university; orthogonality relations, tensor products, the Artin–Wedderburn theorem, and so on. We
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Modules, of modules, and the stable and derived categories. We start with projective modules, and then look at vertices and sources. We then consider the Green correspondence. We define Morita equivalences then study endotrivial modules. Finally we looks at extensions, stable equivalences and then derived e
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The Local-Global Principle,ach of Brauer’s height-zero conjecture, the McKay and Alperin–McKay conjectures, Alperin’s weight conjecture, Broué’s abelian defect group conjecture, Donovan’s and Puig’s conjectures, Feit’s conjecture, and finally Brauer’s .(.)-conjecture. In each case we summarize what is known about the conjectu
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Blocks with Cyclic Defect Groups,he decomposition matrix of the block, then Ext. between simple modules in the block, and indeed the Morita equivalence type of the block (but not the source algebra). We then construct Brauer tree algebras, which are basic algebras that are Morita equivalent to blocks with cyclic defect groups. Afte
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