Unipotent centralizers in algebraic groups.
type: Item
instance of: scholarly article
title: Unipotent centralizers in algebraic groups.
zbMATH Open document ID: 1078.20051
author: Gary M. Seitz
published in: Journal of Algebra
publication date: 2004-11-22T00:00:00Z
review text: Let \(G\) be a simple algebraic group over an algebraically closed field \(K\) of characteristic \(p>0\) with \(p\) a good prime for \(G\). Let \(u\in G\) be unipotent. Canonical embeddings of \(u\) in Abelian unipotent subgroups are studied to obtain results about \(C_G(u)\) -- in particular, \(Z(C_G(u))\) and the reductive part of \(C_G(u)\). In earlier work of the author, the case where \(u\) has order \(p\) was studied and some very elegant results obtained. It turns out that there is a \(1\)-dimensional torus \(T\) acting without fixed points on the connected component \(A\) of \(Z(C_G(u))\) and that \(A\) decomposes nicely as a \(T\)-module. This enables one to reveal many properties of \(C_G(u)\) in a very natural setting.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E45
zbMATH DE Number: 2117266
zbMATH Keywords: unipotent elements
zbMATH Keywords: algebraic groups
zbMATH Keywords: centralizers
zbMATH Keywords: unipotent subgroups
zbMATH Keywords: connected components
reviewed by: Robert Guralnick
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.11.003
OpenAlex ID: W1978731105
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DOI: 10.1016/J.JALGEBRA.2003.11.003
description: scientific article; zbMATH DE number 2117266