Introduction to Representation Theory
内容简介
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory.
The goal of this book is to give a “holistic” introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints.
The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
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作者简介
Pavel Etingof: Massachusetts Institute of Technology, Cambridge, MA,
Oleg Golberg, Sebastian Hensel: Universität Bonn, Bonn, Germany,
Tiankai Liu: Massachusetts Institute of Technology, Cambridge, MA,
Alex Schwendner: Two Sigma Investments, New York, NY,
Dmitry Vaintrob: Harvard University, Cambridge, MA,
Elena Yudovina: University of Cambridge, Cambridge, United Kingdom
with historical interludes by Slava Gerovitch, Massachusetts Institute of Technology, Cambridge, MA
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目录
Cover 1
Title page 2
Contents 4
Introduction 10
Basic notions of representation theory 14
General results of representation theory 50
Representations of finite groups: Basic results 68
Representations of finite groups: Further results 100
Quiver representations 154
Introduction to categories 186
Homological algebra 210
Structure of finite dimensional algebras 218
References for historical interludes 226
Bibliography 232
Index 234
Back Cover 240
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读书文摘
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