Maximality of compression semigroups
type: Item
instance of: scholarly article
title: Maximality of compression semigroups
zbMATH Open document ID: 0824.22006
DOI: 10.1007/BF02573517
published in: Semigroup Forum
publication date: 1995-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/135379
review text: Let \(G\) be a connected semisimple Lie group and \(\tau\) an involution on \(G\). Further let \(L\) be an open subgroup of the group \(G^ \tau\) of \(\tau\)-fixed points and \(P \subset G\) a parabolic subgroup. The semigroup \(S(L,P) = \{g \in G : gLP \subset LP\}\) is called the compression semigroup for \(L\)-orbits of the base point in the flag manifold \(G/P\). The authors prove that compression semigroups for regular symmetric pairs are maximal semigroups. This result explains why in applications one often finds them naturally, for instance when studying maximal domains of extensions of representations.
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 736954
zbMATH Keywords: connected semisimple Lie group
zbMATH Keywords: involution
zbMATH Keywords: flag manifold
zbMATH Keywords: compression semigroups
zbMATH Keywords: regular symmetric pairs
zbMATH Keywords: maximal semigroups
zbMATH Keywords: extensions of representations
author: Joachim Hilgert
author: Karl-Hermann Neeb
reviewed by: A. K. Guts
MaRDI profile type: Publication
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OpenAlex ID: W2054813228
description: scientific article; zbMATH DE number 736954