| Softcover ISBN: | 978-0-8218-4132-7 |
| Product Code: | STML/36 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-2147-2 |
| Product Code: | STML/36.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-4132-7 |
| eBook: ISBN: | 978-1-4704-2147-2 |
| Product Code: | STML/36.B |
| List Price: | $108.00 $83.50 |
| Softcover ISBN: | 978-0-8218-4132-7 |
| Product Code: | STML/36 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-2147-2 |
| Product Code: | STML/36.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-4132-7 |
| eBook ISBN: | 978-1-4704-2147-2 |
| Product Code: | STML/36.B |
| List Price: | $108.00 $83.50 |
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Book DetailsStudent Mathematical LibraryVolume: 36; 2007; 314 ppMSC: Primary 13; Secondary 20
This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.
ReadershipUndergraduate and graduate students interested in invariant theory and its applications.
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Table of Contents
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Chapters
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1. Introduction
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Part 1. Recollections
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Chapter 1. Linear representations of finite groups
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Chapter 2. Rings and algebras
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Part 2. Introduction and Göbel’s bound
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Chapter 3. Rings of polynomial invariants
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Chapter 4. Permutation representations
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Application: Decay of a spinless particle
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Application: Counting weighted graphs
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Part 3. The first fundamental theorem of invariant theory and Noether’s bound
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Chapter 5. Construction of invariants
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Chapter 6. Noether’s bound
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Chapter 7. Some families of invariants
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Application: Production of fibre composites
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Application: Gaussian quadrature
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Part 4. Noether’s theorems
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Chapter 8. Modules
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Chapter 9. Integral dependence and the Krull relations
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Chapter 10. Noether’s theorems
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Application: Self-dual codes
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Part 5. Advanced counting methods and the Shephard-Todd-Chevalley theorem
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Chapter 11. Poincaré series
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Chapter 12. Systems of parameters
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Chapter 13. Pseudoreflection representations
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Application: Counting partitions
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Appendix A. Rational invariants
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Additional Material
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Reviews
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...a large part of the book is written in a friendly style and all notions are carefully explained and immediately demonstrated in concrete examples. Each chapter contains a lot of exercises.
EMS Newsletter -
All together, the expostion of the book under review stands out by its masterly clarity, comprehensiveness, profundity, and didactical disposition. The author has conclusively demonstrated that invariant theory can be taught from scratch, in a student-friendly manner, and by exhibiting both its fascinating beauty and its broad feasibility to very beginners in the field. In this fashion, the present book is fairly unique in the literature on introductory invariant theory.
Zentralblatt MATH -
If you are an undergraduate, or first-year graduate student, and you love algebra, certainly you will enjoy this book, and you will learn a lot from it. It is pleasant reading, and it is self-contained. I strongly recommend this book for an advanced undergraduate or first-year graduate course, and also for independent study.
MAA Online -
Most of the examples and applications are based on recent work of students. This makes the reading of this book very pleasant. Necessary basic information is recalled throughout the book. In addition, all the examples are extremely well detailed. For these two reasons, although some results are recent and subtle, this book seems to be quite appropriate for advanced undergraduate or first-year graduate level courses.
Anne Moreau for Mathematical Reviews
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RequestsReview Copy – for publishers of book reviewsPermission – 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
This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.
Undergraduate and graduate students interested in invariant theory and its applications.
-
Chapters
-
1. Introduction
-
Part 1. Recollections
-
Chapter 1. Linear representations of finite groups
-
Chapter 2. Rings and algebras
-
Part 2. Introduction and Göbel’s bound
-
Chapter 3. Rings of polynomial invariants
-
Chapter 4. Permutation representations
-
Application: Decay of a spinless particle
-
Application: Counting weighted graphs
-
Part 3. The first fundamental theorem of invariant theory and Noether’s bound
-
Chapter 5. Construction of invariants
-
Chapter 6. Noether’s bound
-
Chapter 7. Some families of invariants
-
Application: Production of fibre composites
-
Application: Gaussian quadrature
-
Part 4. Noether’s theorems
-
Chapter 8. Modules
-
Chapter 9. Integral dependence and the Krull relations
-
Chapter 10. Noether’s theorems
-
Application: Self-dual codes
-
Part 5. Advanced counting methods and the Shephard-Todd-Chevalley theorem
-
Chapter 11. Poincaré series
-
Chapter 12. Systems of parameters
-
Chapter 13. Pseudoreflection representations
-
Application: Counting partitions
-
Appendix A. Rational invariants
-
...a large part of the book is written in a friendly style and all notions are carefully explained and immediately demonstrated in concrete examples. Each chapter contains a lot of exercises.
EMS Newsletter -
All together, the expostion of the book under review stands out by its masterly clarity, comprehensiveness, profundity, and didactical disposition. The author has conclusively demonstrated that invariant theory can be taught from scratch, in a student-friendly manner, and by exhibiting both its fascinating beauty and its broad feasibility to very beginners in the field. In this fashion, the present book is fairly unique in the literature on introductory invariant theory.
Zentralblatt MATH -
If you are an undergraduate, or first-year graduate student, and you love algebra, certainly you will enjoy this book, and you will learn a lot from it. It is pleasant reading, and it is self-contained. I strongly recommend this book for an advanced undergraduate or first-year graduate course, and also for independent study.
MAA Online -
Most of the examples and applications are based on recent work of students. This makes the reading of this book very pleasant. Necessary basic information is recalled throughout the book. In addition, all the examples are extremely well detailed. For these two reasons, although some results are recent and subtle, this book seems to be quite appropriate for advanced undergraduate or first-year graduate level courses.
Anne Moreau for Mathematical Reviews
