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Polynomial Invariants of Finite Groups

Polynomial Invariants of Finite Groups

$62.00

Part of London Mathematical Society Lecture Note Series

  • Date Published: October 1993
  • availability: Available
  • format: Paperback
  • isbn: 9780521458863

$ 62.00
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  • 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.

    • First book on this subject
    • Includes up-to-the minute research
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    Product details

    • Date Published: October 1993
    • format: Paperback
    • isbn: 9780521458863
    • length: 132 pages
    • dimensions: 229 x 152 x 8 mm
    • weight: 0.21kg
    • availability: 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.

  • Author

    D. J. Benson

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