Introduction to Representation Theory
About this Title
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 and Elena Yudovina, University of Cambridge, Cambridge, United Kingdom
Publication: The Student Mathematical Library
Publication Year 2011: Volume 59
ISBNs: 978-0-8218-5351-1 (print); 978-1-4704-1222-7 (online)
MathSciNet review: MR2808160
MSC: Primary 20G15; Secondary 16-01, 16G10, 17B10, 20-01
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.
Undergraduate and graduate students interested in algebra and representation theory.
Table of Contents
- Chapter 1. Introduction
- Chapter 2. Basic notions of representation theory
- Chapter 3. General results of representation theory
- Chapter 4. Representations of finite groups: Basic results
- Chapter 5. Representations of finite groups: Further results
- Chapter 6. Quiver representations
- Chapter 7. Introduction to categories
- Chapter 8. Homological algebra
- Chapter 9. Structure of finite dimensional algebras