Softcover ISBN:  9780821853511 
Product Code:  STML/59 
List Price:  $48.00 
Individual Price:  $38.40 
Electronic ISBN:  9781470412227 
Product Code:  STML/59.E 
List Price:  $45.00 
Individual Price:  $36.00 

Book DetailsStudent Mathematical LibraryVolume: 59; 2011; 228 ppMSC: Primary 16; 20;
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.ReadershipUndergraduate and graduate students interested in algebra and representation theory.

Table of Contents

Chapters

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


Additional Material

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 wellwritten, 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


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 Book Details
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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.

Chapters

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

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 wellwritten, 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