Polynomial Invariants of Finite Groups / D. J. Benson.
Material type: TextSeries: London Mathematical Society Lecture Note Series ; no. 190Publisher: Cambridge : Cambridge University Press, 1993Description: 1 online resource (132 pages) : digital, PDF file(s)Content type: text Media type: computer Carrier type: online resourceISBN: 9780511565809 (ebook)Subject(s): Invariants | Finite groups | Divisor theory | Groups (Mathematics)Additional physical formats: Print version: : No titleDDC classification: 512./5 LOC classification: QA201 | .B46 1993Online resources: Click here to access online Summary: 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.Current library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK12189 |
Title from publisher's bibliographic system (viewed on 16 Oct 2015).
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.
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