Polynomial Invariants of Finite Groups [Paperback]

This is the first book to deal with invariant theory and the representations of finite groups.Heavy use is made of techniques from commutative algebra in this 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, a topic of great interest in abstract algebra.Heavy use is made of techniques from commutative algebra in this 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, a topic of great interest in abstract algebra.This book covers a topic of great interest in abstract algebra. It gives 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. Heavy use is made of techniques from commutative algebra, and these are developed as needed. Special attention is paid to the role played by pseudoreflections, which arise because they correspond to the divisors in the polynomial ring that ramify over the invariants. The author includes the recent proof of the Carlisle-Kropholler conjecture.1. Finite generation of invariants; 2. Poincar? 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. ...not only complete, it is written with a view to its being consulted on page 49 without having read up to page 48. It contains a wealth of material in updated form which should give a great impulse to further work, for example, an account of Dickson's work on invariants under the classical groups over finite fields. G.-C. Rota, Bulletin of Mathematics Books ...The exposition is uniformly excellent. It il£0