**Student Mathematical Library**

Volume: 59;
2011;
228 pp;
Softcover

MSC: Primary 16; 20;

Print ISBN: 978-0-8218-5351-1

Product Code: STML/59

List Price: $45.00

Individual Price: $36.00

**Electronic ISBN: 978-1-4704-1222-7
Product Code: STML/59.E**

List Price: $45.00

Individual Price: $36.00

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#### Supplemental Materials

# Introduction to Representation Theory

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*Pavel Etingof; Oleg Golberg; Sebastian Hensel; Tiankai Liu; Alex Schwendner; Dmitry Vaintrob; Elena Yudovina*

with historical interludes by

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.

#### Table of Contents

# Table of Contents

## Introduction to Representation Theory

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Introduction 110 free
- Basic notions of representation theory 514 free
- General results of representation theory 4150
- Representations of finite groups: Basic results 5968
- Representations of finite groups: Further results 91100
- Quiver representations 145154
- Introduction to categories 177186
- Homological algebra 201210
- Structure of finite dimensional algebras 209218
- References for historical interludes 217226
- Bibliography 223232
- Index 225234 free
- Back Cover Back Cover1240

#### Readership

Undergraduate and graduate students interested in algebra and representation theory.

#### Reviews

This charming book ... the material in the book is quite modern, the unifying theme being the representation theory of associative algebras, and the presentation is very accessible. ...It is a truly wonderful achievement. The book is well-written, sportingly paced, and brims with mathematical elegance: the prose is clear and tight and the proofs are compact and pretty.

-- MAA Reviews

The book gives a concise introduction to various aspects of representation theory. It is an interesting addition to the existing literature on the subject.

-- Mathematical Reviews

Add to this the sets of problems included in the book, replete with occasional hints and estimates of the degree of difficulty, as well as the wonderful 'Historical Interludes' by Slava Gerovitch, and the result is a fantastic little book. I think it is bound to become the way to get into this subject 'holistically.'

-- MAA Reviews