On the invariant theory of finite pseudo reflection groups
type: Item
instance of: scholarly article
title: On the invariant theory of finite pseudo reflection groups
zbMATH Open document ID: 0576.20032
DOI: 10.1007/BF01237854
author: Larry Smith
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: The author gives a short noncomputational proof of a result of \textit{G. C. Shephard} and \textit{J. A. Todd} [Can. J. Math. 6, 274--304 (1954; Zbl 0055.14305)] and of \textit{C. Chevalley} [Am. J. Math. 77, 778--782 (1955; Zbl 0065.26103)]: \(G\leq \mathrm{GL}(V)\) is a finite group generated by pseudo reflections, where \(V\) is a vector space over the field \(k\), and assume \(\mathrm{char}\,k\nmid | G|\). Extend the action of \(G\) to the polynomial algebra on the vector space \(V\). Then the subring of invariant polynomials is isomorphic to a polynomial algebra.
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 3920792
zbMATH Keywords: finite group generated by pseudo reflections
zbMATH Keywords: invariant polynomials
zbMATH Keywords: polynomial algebra
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
cites work: Q5580319
cites work: Invariants of Finite Groups Generated by Reflections
cites work: Finite Unitary Reflection Groups
cites work: Homology of Noetherian rings and local rings
description: scientific article; zbMATH DE number 3920792