Nilpotent variety of a reductive monoid.
type: Item
instance of: scholarly article
title: Nilpotent variety of a reductive monoid.
zbMATH Open document ID: 1146.20047
published in: Journal of Algebraic Combinatorics
publication date: 2008-06-03T00:00:00Z
review text: An irreducible linear algebraic monoid \(M\) with zero is referred to as reductive if its unit group is so; \(M\) is semisimple if it is reductive with \(1\)-dimensional center. The author studies the nilpotent vatiety \(M_{\text{nil}}:=\{a\in M\mid a^n=0\text{ for some }n\}\). In general this variety can be reducible and has a completely different structure from the unipotent variety of the unit group \(G\) of \(M\). When \(M\) is \(\mathcal J\)-irreducible or \(\mathcal J\)-coirreducible, the author obtains a precise description of the irreducible components of \(M_{\text{nil}}\) via the Renner monoid of \(M\) and the Weyl group of \(G\). In particular, the author finds necessary and sufficient conditions for the nilpotent variety to be irreducible.
reviewed by: Huang Wenxue
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 5281979
zbMATH Keywords: \(\mathcal J\)-coirreducible monoids
zbMATH Keywords: \(\mathcal J\)-irreducible monoids
zbMATH Keywords: nilpotent varieties
zbMATH Keywords: Renner monoids
zbMATH Keywords: reductive monoids
zbMATH Keywords: semisimple monoids
zbMATH Keywords: unipotent varieties
zbMATH Keywords: Weyl groups
author: Mohan S. Putcha
MaRDI profile type: Publication
full work available at URL: s10801-007-0087-y
OpenAlex ID: W2080169761
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DOI: 10.1007/S10801-007-0087-Y
description: scientific article; zbMATH DE number 5281979