Semigroups in symmetric Lie groups (Q2381842)

Let \(G\) be a Lie group and \(L\) a closed subgroup of \(G\). The authors consider left \(L\)-invariant subsemigroups \(S\). More precisely, they study conditions under which such semigroups have to be all of \(G\). Unless \(S=L\), this is the case for instance if \(G\) is simple and \(L\) is maximal compactly embedded in \(G\) (e.g. maximal compact, if \(G\) has finite center). For more general symmetric subgroups one can give conditions in terms of the standard parabolic for which \(L\) is the Levi part. On the way to prove these results the authors provide several sufficient conditions for \(S\) to have non-empty interior in \(G\).