On subsemigroups of semisimple Lie groups (Q5970605)

Let \(G\) be a connected semisimple Lie group and \(S\) a subsemigroup of \(G\). Suppose that \(\mathfrak g\) is the Lie algebra of \(G\) and \({\mathfrak g}={\mathfrak k}+{\mathfrak p}\) a Cartan decomposition. The authors prove that \(S\) is a group if it is biinvariant under the analytic subgroup \(K\) of \(G\) with Lie algebra \(\mathfrak k\). Since in the simple case \(K\) is a maximal subgroup of \(G\), the subgroups containing \(K\) are easily determined, so the result gives a complete classification of \(K\)-biinvariant subsemigroups.