Polynomial Invariant of Finite Groups

Erscheinungsjahr 1993
ISBN: 978-0-521-45886-3
Verlag: Cambridge University Press

Buch, Englisch, Band 190, 128 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 203 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Benson, D. J.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

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.