with historical interludes by Slava Gerovitch, Massachusetts Institute of Technology, Cambridge, MA
| Softcover ISBN: | 978-0-8218-5351-1 |
| Product Code: | STML/59 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-1222-7 |
| Product Code: | STML/59.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-5351-1 |
| eBook: ISBN: | 978-1-4704-1222-7 |
| Product Code: | STML/59.B |
| List Price: | $108.00 $83.50 |
with historical interludes by Slava Gerovitch, Massachusetts Institute of Technology, Cambridge, MA
| Softcover ISBN: | 978-0-8218-5351-1 |
| Product Code: | STML/59 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-1222-7 |
| Product Code: | STML/59.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-5351-1 |
| eBook ISBN: | 978-1-4704-1222-7 |
| Product Code: | STML/59.B |
| List Price: | $108.00 $83.50 |
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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.
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Table of Contents
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Chapters
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Chapter 1. Introduction
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Chapter 2. Basic notions of representation theory
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Chapter 3. General results of representation theory
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Chapter 4. Representations of finite groups: Basic results
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Chapter 5. Representations of finite groups: Further results
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Chapter 6. Quiver representations
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Chapter 7. Introduction to categories
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Chapter 8. Homological algebra
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Chapter 9. Structure of finite dimensional algebras
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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 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
