Polynomial Invariants of Finite Groups

This is the first book to deal with invariant theory and the representations of finite groups.

D. J. Benson (Author)

9780521458863, Cambridge University Press

Paperback, published 7 October 1993

132 pages
22.9 x 15.2 x 0.8 cm, 0.21 kg

"...The exposition is uniformly excellent. It is also worth observing that many important ideas in modern commutative algebra were developed in connection with invariant theory and arise in the proofs cited...The author gives detailed, textbook-like explanations of all of these. As is customary for books published by Cambridge University Press in this series, the typography sets a standard of excellence and the price is remarkably low." Frank Grosshans, Mathematical Reviews

This is the first book to deal with invariant theory and the representations of finite groups. By restricting attention to finite groups Dr Benson is able to avoid recourse to the technical machinery of algebraic groups, and he develops the necessary results from commutative algebra as he proceeds. Thus the book should be accessible to graduate students. In detail, the book contains an account of invariant theory for the action of a finite group on the ring of polynomial functions on a linear representation, both in characteristic zero and characteristic p. Special attention is paid to the role played by pseudoreflections, which arise because they correspond to the divisors in the polynomial ring which ramify over the invariants. Also included is a new proof by Crawley-Boevey and the author of the Carlisle-Kropholler conjecture. This volume will appeal to all algebraists, but especially those working in representation theory, group theory, and commutative or homological algebra.

1. Finite generation of invariants
2. Poincaré series
3. Divisor classes, ramification and hyperplanes
4. Homological properties of invariants
5. Polynomial tensor exterior algebra
6. Polynomial rings and regular local rings
7. Groups generated by pseudoreflections
8. Modular invariants
Appendices
Bibliography
Index.

Subject Areas: Groups & group theory [PBG]