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Author : D. J. Benson
Release : 1993-10-07
Genre : Mathematics
Kind : eBook
Book Rating : 863/5 ( reviews)
Book Synopsis Polynomial Invariants of Finite Groups by : D. J. Benson
Download or read book Polynomial Invariants of Finite Groups written by D. J. Benson. This book was released on 1993-10-07. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to deal with invariant theory and the representations of finite groups.
Author : David J. Benson
Release : 2014-05-14
Genre : MATHEMATICS
Kind : eBook
Book Rating : 031/5 ( reviews)
Book Synopsis Polynomial Invariants of Finite Groups by : David J. Benson
Download or read book Polynomial Invariants of Finite Groups written by David J. Benson. This book was released on 2014-05-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Larry Smith
Release : 1995-04-15
Genre : Mathematics
Kind : eBook
Book Rating : 470/5 ( reviews)
Book Synopsis Polynomial Invariants of Finite Groups by : Larry Smith
Download or read book Polynomial Invariants of Finite Groups written by Larry Smith. This book was released on 1995-04-15. Available in PDF, EPUB and Kindle. Book excerpt: Written by an algebraic topologist motivated by his own desire to learn, this well-written book represents the compilation of the most essential and interesting results and methods in the theory of polynomial invariants of finite groups. From the table of contents: - Invariants and Relative Invariants - Finite Generation of Invariants - Constructio
Author :
Release : 1997-06-01
Genre : Mathematics
Kind : eBook
Book Rating : 179/5 ( reviews)
Book Synopsis Polynomial Invariants of Finite Groups by :
Download or read book Polynomial Invariants of Finite Groups written by . This book was released on 1997-06-01. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mara D. Neusel
Release : 2010-03-08
Genre : Mathematics
Kind : eBook
Book Rating : 816/5 ( reviews)
Book Synopsis Invariant Theory of Finite Groups by : Mara D. Neusel
Download or read book Invariant Theory of Finite Groups written by Mara D. Neusel. This book was released on 2010-03-08. Available in PDF, EPUB and Kindle. Book excerpt: The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.
