The Bookpointindia

About the BookAbout the Author(s)Table of Contents

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.

Mara D. Neusel : Texas Tech University, Lubbock, TX

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