Cargando…
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 |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
©1993.
|
| Colección: | London Mathematical Society lecture note series ;
190. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn836870322 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 130408s1993 enk ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d E7B |d OCLCO |d COO |d OCLCF |d YDXCP |d OCLCQ |d AGLDB |d HEBIS |d OCLCO |d UAB |d OCLCQ |d VTS |d OCLCA |d REC |d OCLCO |d M8D |d OCLCO |d SFB |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO | ||
| 019 | |a 797839839 | ||
| 020 | |a 9781107362031 |q (electronic bk.) | ||
| 020 | |a 1107362032 |q (electronic bk.) | ||
| 020 | |z 0521458862 | ||
| 020 | |z 9780521458863 | ||
| 020 | |z 9780511565809 | ||
| 029 | 1 | |a DEBBG |b BV043083237 | |
| 029 | 1 | |a DEBSZ |b 421267143 | |
| 029 | 1 | |a GBVCP |b 804535264 | |
| 035 | |a (OCoLC)836870322 |z (OCoLC)797839839 | ||
| 050 | 4 | |a QA201 |b .B46 1993eb | |
| 072 | 7 | |a MAT |x 002050 |2 bisacsh | |
| 082 | 0 | 4 | |a 512./5 |2 22 |
| 084 | |a 31.21 |2 bcl | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Benson, D. J. |q (David J.), |d 1955- | |
| 245 | 1 | 0 | |a Polynomial invariants of finite groups / |c D.J. Benson. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c ©1993. | ||
| 300 | |a 1 online resource (ix, 118 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series ; |v 190 | |
| 504 | |a Includes bibliographical references (pages 109-115) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Invariants. | |
| 650 | 0 | |a Finite groups. | |
| 650 | 0 | |a Divisor theory. | |
| 650 | 6 | |a Invariants. | |
| 650 | 6 | |a Groupes finis. | |
| 650 | 6 | |a Théorie des diviseurs. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Divisor theory |2 fast | |
| 650 | 7 | |a Finite groups |2 fast | |
| 650 | 7 | |a Invariants |2 fast | |
| 650 | 7 | |a Endliche Gruppe |2 gnd | |
| 650 | 7 | |a Invariante |2 gnd | |
| 650 | 7 | |a Invariantentheorie |2 gnd | |
| 650 | 1 | 7 | |a Eindige groepen. |2 gtt |
| 650 | 7 | |a Invariants. |2 ram | |
| 650 | 7 | |a Groupes finis. |2 ram | |
| 650 | 7 | |a Diviseurs, Théorie des. |2 ram | |
| 650 | 7 | |a Groupes de classes (Mathématiques) |2 ram | |
| 653 | 0 | |a Groups (Mathematics) | |
| 776 | 0 | 8 | |i Print version: |a Benson, D.J. (David J.), 1955- |t Polynomial invariants of finite groups. |d Cambridge ; New York : Cambridge University Press, ©1993 |z 0521458862 |w (DLC) 94211280 |w (OCoLC)29409678 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 190. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552411 |z Texto completo |
| 938 | |a ebrary |b EBRY |n ebr10562300 | ||
| 938 | |a EBSCOhost |b EBSC |n 552411 | ||
| 938 | |a YBP Library Services |b YANK |n 10405630 | ||
| 994 | |a 92 |b IZTAP | ||