Polynomial Invariants of Finite Groups: 190 (London Mathematical Society Lecture Note Series, Series Number 190) - Softcover

Benson, D. J.

Softcover

ISBN 10: 0521458862 ISBN 13: 9780521458863

Publisher: Cambridge University Press, 1993

Synopsis

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.

About this title

Review

"...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 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

Book 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. This volume will appeal to all algebraists, but especially those working in representation theory, group theory, and commutative or homological algebra.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1993
• Language: English
• ISBN 10: 0521458862
• ISBN 13: 9780521458863
• Binding: Paperback
• Number of pages: 128