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Introduction to Representation Theory

Pavel Etingof Massachusetts Institute of Technology, Cambridge, MA
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
Available Formats:
Softcover ISBN: 978-0-8218-5351-1
Product Code: STML/59
List Price: $48.00 Individual Price:$38.40
Electronic ISBN: 978-1-4704-1222-7
Product Code: STML/59.E
List Price: $45.00 Individual Price:$36.00
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List Price: $72.00 Click above image for expanded view Introduction to Representation Theory Pavel Etingof Massachusetts Institute of Technology, Cambridge, MA 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 Available Formats:  Softcover ISBN: 978-0-8218-5351-1 Product Code: STML/59  List Price:$48.00 Individual Price: $38.40  Electronic ISBN: 978-1-4704-1222-7 Product Code: STML/59.E  List Price:$45.00 Individual Price: $36.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$72.00
• Book Details

Student Mathematical Library
Volume: 592011; 228 pp
MSC: 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.

• 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

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 592011; 228 pp
MSC: 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.

• 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 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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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