INVARIANT CONES FOR SEMIGROUPS IN TRANSITIVE LIE GROUPS

摘要

Let G be a connected Lie group which has a transitive representation on R{sup}n and S {is contained in} G be a semigroup with a nonempty interior. We study necessary and sufficient conditions for the existence of the S-invariant pointed and generating cone W{is contained in}R{sup}n, where the parabolic type of S arises as a central concept.