Polynomial Invariants of Finite Groups
Polynomial Invariants of Finite Groups
$55.99
USDThis 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.
- First book on this subject
- Includes up-to-the minute research
Reviews & endorsements
"...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
Product details
October 1993Paperback
9780521458863
132 pages
229 × 152 × 8 mm
0.21kg
Available
Table of Contents
- 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.
