Some rings of differential operators for \(\text{Sl}_ 2\)-invariants are simple
type: Item
instance of: scholarly article
title: Some rings of differential operators for \(\text{Sl}_ 2\)-invariants are simple
zbMATH Open document ID: 0871.16014
DOI: 10.1016/0022-4049(95)00072-0
author: Michel Van den Bergh
published in: Journal of Pure and Applied Algebra
publication date: 1997-08-05T00:00:00Z
review text: Let \(A\) be a finitely generated \(\mathbb{C}\)-algebra and \(G\) a reductive group acting on \(X=\text{Spec }A\). Assume that \(X\) is smooth and connected. Then it is conjectured that the ring of differential operators of the invariant ring \(A^G\) is a simple ring. In this paper some new tools are introduced which are useful to prove this conjecture in some special cases. In particular it is proved if \(G=\text{SL}_2\) and \(X\) is a reducible \(G\)-module \(M\) such that each irreducible component of the representation \(M\) has even dimension.
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 13A50
zbMATH DE Number: 908496
zbMATH Keywords: reductive groups
zbMATH Keywords: rings of differential operators of invariant rings
zbMATH Keywords: simple rings
zbMATH Keywords: reducible modules
reviewed by: Stefan Helmke
MaRDI profile type: Publication
full work available at URL: 0022-4049(95)00072-0
OpenAlex ID: W2052593592
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description: scientific article; zbMATH DE number 908496