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Polynomial Invariants of Finite Groups (Universitext)

# Polynomial Invariants of Finite Groups (Universitext)

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Published by Springer-Verlag .
Written in English

The Physical Object
FormatPaperback
Number of Pages350
ID Numbers
Open LibraryOL12776809M
ISBN 103540571175
ISBN 109783540571179

Project Euclid - mathematics and statistics online. Algebr. Geom. Topol. Vol Number 2 (), Finite-type invariants of w-knotted objects, I: w-knots and the Alexander polynomial. In mathematics, the Chevalley–Shephard–Todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated by the case of subgroups of the complex general linear group the theorem was first proved by G. C. Shephard and J. A. Todd () who gave a.

Next, we examine relationship between polynomial invariants and Galois extensions of ﬁelds. Let K/k be a ﬁeld extension, and H a Hopf algebra over -form of H we mean a Hopf algebra A over k such that H ∼= AK = A⊗K as K-Hopf algebras[1, p]. Theorem 7. Let K/k be a ﬁnite Galois extension of ﬁelds, and H a semisimple and. LIFTING MAPPINGS OVER INVARIANTS OF FINITE GROUPS Andreas Kriegl, Mark Losik, Peter W. Michor, Armin Rainer Abstract. We characterize those regular, holomorphic or formal maps int.

Words and polynomial invariants of ﬁnite groups in non-commutative variables When the group G is generated by pseudo-reﬂectionsacting on a vector space V, then if V is simple, V is called the geometric G-module. WhenG is the symmetric group Sn on n letters and acts on the vector spaceV spannedbythevectors{x 1,x. Find many great new & used options and get the best deals for London Mathematical Society Lecture Note Ser.: Polynomial Invariants of Finite Groups by D. J. Benson (, Trade Paperback) at the best online prices at eBay! Free shipping for many products!

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### Polynomial Invariants of Finite Groups (Universitext) Download PDF EPUB FB2

This book covers a topic of great interest in abstract algebra. It gives 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.

Heavy use is made of techniques from commutative algebra, and these are developed as by:   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 by:   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 - ConstructioCited by:   Polynomial Invariants of Finite Groups by D.

Benson,available at Book Depository with free delivery : D. Benson. Polynomial Invariants of Finite Groups. Benson. Cambridge University Press, Oct 7, - Mathematics - pages.

0 Reviews. This is the first book to deal with invariant theory and the representations 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.

Thus the book should be accessible to graduate students. In detail, the book contains an account. Polynomial invariants of finite groups Larry Smith 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.

Polynomial Invariants of Finite Groups book. Polynomial Invariants of Finite Groups. DOI link for Polynomial Invariants of Finite Groups.

Polynomial Invariants of Finite Groups book. By Larry Smith. Edition 1st Edition. First Published eBook Published 15 April Author: Larry Smith. Invariants and Relative Invariants 2. Finite Generation of Invariants 3. Construction of Invariants 4. Poincare Series 5. Dimension Theoretic Properties of Rings of Invariants 6.

Homological Properties of Invariants 7. Groups Generated by Reflections 8. Modular Invariants 9. Polynomial.

In the recently published book , the authors summarized the effort to determine the struc- tures of the invariant rings of all finite irreducible reflection groups. First on p. a table showing which group has a polynomial ring of invariants is given (cf.

).Cited by: 7. @book {bensonpoly, MRKEY = {}, AUTHOR = {Benson, David J.}, TITLE = {Polynomial Invariants of Finite Groups}, SERIES = {London Math. Soc. Lecture Note Ser.}. This book covers a topic of great interest in abstract algebra. It gives 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.

Heavy use is made of techniques from commutative algebra, and these are developed as needed. Special attention is paid to the role played by. Broué M. () Polynomial Invariants of Finite Linear Groups.

In: Introduction to Complex Reflection Groups and Their Braid Groups. Lecture Notes in Mathematics, vol Download Citation | Polynomial invariants of finite unitary groups | Let Un(Fq2) be the n-dimensional unitary group over the finite field Fq2.

In this paper, we find explicit generators and. The book includes a dedicated chapter on graded representations and applications of polynomial invariants of finite groups, and its closing chapter addresses the more recent notion of the Drinfeld double of a finite group and the corresponding representation of GL_2(Z).

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. 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. Get this from a library. Polynomial invariants of finite groups. [D J Benson] -- 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. ISBN: OCLC Number: Description: ix, pages ; 23 cm: Contents: 1. Finite Generation of Invariants The basic object of study Noetherian rings and modules Finite groups in arbitrary characteristic Krull dimension and going up and down Noether's bound in characteristic zero Linearly reductive algebraic groups You will also find relevant papers by searching for "polynomial permutation invariants." It falls under the broader rubric of "invariant theory of finite groups", which is a developed field.

See the books by Benson, Smith, Neusel and Smith, Campbell and Wehlau, and Derksen and Kemper. This paper studies separating invariants of finite groups acting on affine varieties through automorphisms.

Several results, proved by Serre, Dufresne, Kac–Watanabe and Gordeev, and Jeffries and Dufresne exist that relate properties of the invariant ring or a separating subalgebra to properties of the group action.The polynomial invariants of finite groups have been studied for more than a century now and continue to find new applications and generate interesting problems.

In this article we will survey some of the recent developments coming primarily from algebraic topology and .Invariant Theory of Finite Groups tral role in the earlier chapters in this book, were proved by Hilbert in the course of his investigations of invariant theory.

In this chapter, we will study the invariants of ﬁnite groups. The basic goal is to Invariant Theory of Finite Groups Deﬁnition 1.

A polynomial f.