On irreducible sl(2,\({\mathbb{R}})\)-modules and \(sl_ 2\)-triples
type: Item
instance of: scholarly article
title: On irreducible sl(2,\({\mathbb{R}})\)-modules and \(sl_ 2\)-triples
zbMATH Open document ID: 0708.17023
DOI: 10.1007/BF02573270
author: Norbert Dörr
published in: Semigroup Forum
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135022
review text: The purpose of this paper is twofold. On one hand it describes the way sl(2,\({\mathbb{R}})\) appears as subalgebra of other finite-dimensional real Lie algebras by means of compactly embedded Cartan subalgebras and the corresponding root decompositions. On the other hand it describes the action of sl(2,\({\mathbb{R}})\) on its irreducible finite-dimensional modules by means of a basis \(\{\) T,H,U\(\}\) of sl(2,\({\mathbb{R}})\) with \([U,T]=2H\), \([U,H]=-2T\) and \([T,H]=-2U.\) This work is motivated by the study of subsemigroups of real Lie groups and the corresponding invariant cones in the Lie algebras.
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 4163120
zbMATH Keywords: irreducible module
zbMATH Keywords: real Lie algebras
zbMATH Keywords: invariant cones
reviewed by: Alberto Elduque
MaRDI profile type: Publication
cites work: Q5614712
cites work: Q4095018
cites work: Volterra algebra and the Bethe–Salpeter equation
cites work: Q4693080
cites work: Old and new on Sl(2)
cites work: Invariant cones in Lie algebras
OpenAlex ID: W1981569568
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description: scientific article; zbMATH DE number 4163120