Polynomial invariants of finite groups
By: D.J. Benson.
Series: London Mathematical Society lecture note series ;; 190
Publisher: Cambridge University Press
Published: 1993
Place of publication: Cambridge; New York
Language: eng
Number of pages: 118
Subjects: Invariants.; Finite groups.; Divisor theory.
Description: 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 pages 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.
Notes: Includes bibliographical references (p. 109-115) and index.