Equidimensional relatively stable reductive algebraic groups with simple commutator subgroups
type: Item
instance of: scholarly article
title: Equidimensional relatively stable reductive algebraic groups with simple commutator subgroups
zbMATH Open document ID: 0906.20030
author: Haruhisa Nakajima
published in: Proceedings of the Japan Academy. Series A
publication date: 1998-12-07T00:00:00Z
review text: The main result is the following theorem: Let \(G\) be a connected reductive algebraic group over \(\mathbb{C}\) whose commutator subgroup \(G'\) is a simple algebraic group. Let \(V\) be a finite-dimensional algebraic \(G\)-module. Assume that \(V\) is equidimensional and that there is a \(G\)-submodule \(U\) of \(V\) such that the natural action of \(G\) on \(U/ /G\) is stable and the inclusion \(U\hookrightarrow V\) induces an isomorphism \(U/ /G\simeq V/ /G\). Then \(V\) is cofree. -- This result is an indirect consequence of some explicit classifications obtained in this paper combined with further calculations and the known classifications.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 13A50
zbMATH DE Number: 1160717
zbMATH Keywords: connected reductive algebraic groups
zbMATH Keywords: equidimensional representations
zbMATH Keywords: finite-dimensional modules
zbMATH Keywords: stable actions
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: pjaa.73.181
OpenAlex ID: W2066240508
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DOI: 10.3792/PJAA.73.181
description: scientific article; zbMATH DE number 1160717