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Polynomial invariants of finite groups /
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....
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
©1993.
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| Colección: | London Mathematical Society lecture note series ;
190. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Contents; Introduction; 1 Finite Generation of Invariants; 1.1 The basic object of study; 1.2 Noetherian rings and modules; 1.3 Finite groups in arbitrary characteristic; 1.4 Krull dimension and going up and down; 1.5 Noether's bound in characteristic zero; 1.6 Linearly reductive algebraic groups; 2 Poincare series; 2.1 The Hilbert-Serre theorem; 2.2 Noether normalization; 2.3 Systems of parameters; 2.4 Degree and if>; 2.5 Molien's theorem; 2.6 Reflecting hyperplanes; 3 Divisor Classes, Ramification and Hyperplanes; 3.1 Divisors; 3.2 Primes of height one; 3.3 Duality
- 3.4 Reflexive modules3.5 Divisor classes and unique factorization; 3.6 The Picard group; 3.7 The trace; 3.8 Ramification; 3.9 Cl(ii:[V]G); 3.10 The different; 3.11 The homological different; 3.12 A ramification formula; 3.13 The Carlisle-Kropholler conjecture; 4 Homological Properties of Invariants; 4.1 Minimal resolutions; 4.2 Hilbert's syzygy theorem; 4.3 Depth and Cohen-Macaulay rings; 4.4 Homological characterization of depth; 4.5 The canonical module and Gorenstein rings; 4.6 Watanabe's theorem; 5 Polynomial tensor exterior algebras; 5.1 Motivation and first properties
- 5.2 A variation on Molien's theorem5.3 The invariants are graded Gorenstein; 5.4 The Jacobian; 6 Polynomial rings and regular local rings; 6.1 Regular local rings; 6.2 Serre's converse to Hilbert's syzygy theorem; 6.3 Uniqueness of factorization; 6.4 Reflexive modules; 7 Groups Generated by Pseudoreflections; 7.1 Reflections and pseudoreflections; 7.2 The Shephard-Todd theorem; 7.3 A theorem of Solomon; 8 Modular invariants; 8.1 Dickson's theorem; 8.2 The special linear group; 8.3 Symplectic invariants; A Examples over the complex numbers; B Examples over finite fields; Bibliography; Index