On irreducible sl(2,\({\mathbb{R}})\)-modules and \(sl_ 2\)-triples
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.
scientific article; zbMATH DE number 4163120
scientific article