Semigroup actions on adjoint orbits

摘要

Let G be a connected semi-simple Lie group with finite center and S ? G a subsemigroup with intS ≠ φ. In this article we study the control sets for the actions of S on the adjoint orbits Ad(G)H, where H is a regular element in the Lie algebra of G. We show here that these sets can be described as sets of fixed points for regular elements in the interior of S. Moreover, we shall describe the domains of attraction of this control sets and show that these sets are not comparable with respect to the natural order on control sets. Mathematics Subject Classification 2000: 22F30.