Representation Theory of Finite Groups: a Guidebook
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Beschreibung
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.
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.
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 covered in a self-contained fashion
Autor*in
David A. Craven
Themen in »Representation Theory of Finite Groups: a Guidebook«
Group representation Representations of finite groups Representations of symmetric groups Finite groups of Lie type Block theory Modular representation theory Local-global conjectures Blocks with cyclic defect groups
Stimmen zu »Representation Theory of Finite Groups: a Guidebook«
“The book is intended for students and general readers. ... each of the chapters is followed by a series of exercises (83 in all), which are suitable for student seminars.” (A. S. Kondrat'ev, Mathematical Reviews, November, 2020)
“The book is highly recommended for researchers in representation and character theory of finite groups.” (Mohammad-Reza Darafsheh, zbMATH 1446.20002, 2020)
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