Transitive actions of semigroups in semi-simple Lie groups

G

be a connected semi-simple Lie group with finite center and S⊂G a semigroup with interior points. It is proved that S is transitive on a homogenous space G/L only if the action of L on B is minimal and contracting, where B=G/Pis the flag manifold of G asssociated with S. In [5, Thm.6.4] the authors claimed another necessary condition in case G is simple, namely, that L is discrete. It is shown by means of an example that this condition is wrong without the further assumption that G/L is compact.