Invariant theory for wreath product groups
type: Item
instance of: scholarly article
title: Invariant theory for wreath product groups
zbMATH Open document ID: 0972.13006
DOI: 10.1016/S0022-4049(98)00176-5
author: Ana Paula S. Dias
author: Ian Stewart
published in: Journal of Pure and Applied Algebra
publication date: 2001-10-29T00:00:00Z
review text: Invariant theory is an important issue in equivariant bifurcation theory. In the paper the authors develop the invariant theory of wreath products of a compact Lie group with a finite permutation group. For a compact Lie group the authors find the quadratic and cubic equivariants of the wreath product in terms of those of the Lie group and the permutation group. As one of the technical tools the authors prove that the Molien series of the wreath product is determined by the Molien series of the factors. Moreover they obtain homogeneous systems of parameters for rings of invariants and modules of equivariants of wreath products when the Lie group is supposed to be finite. In essence they prove that useful information about the invariants and equivariants of the wreath product can be read off in a simple manner from similar information about the factors. To this end they modify algorithms of \textit{B. Sturmfels} [``Algorithms in invariant theory'', Texts and Monographs in Symbolic Computation (Wien 1993; Zbl 0802.13002)], and of \textit{P. A. Worfolk} [J. Symb. Comput. 17, 487-511 (1994; Zbl 0819.13013)] for the Molien series and Cohen-Macaulay property to the wreath product.
reviewed by: Peter Schenzel
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 20C40
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 1488534
zbMATH Keywords: wreath product
zbMATH Keywords: equivariant bifurcation theory
zbMATH Keywords: Molien series
zbMATH Keywords: compact Lie group
zbMATH Keywords: permutation group
zbMATH Keywords: Cohen-Macaulay property
MaRDI profile type: Publication
full work available at URL: s0022-4049(98)00176-5
OpenAlex ID: W2030650555
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description: scientific article; zbMATH DE number 1488534