Polynomial Invariant of Finite Groups

ISBN-13: 9780521458863 / Angielski / Miękka / 1993 / 132 str.

D. J. Benson

Opis

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.

Recenzje

"...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

Spis treści

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.