Reversibility and transitivity of semigroup actions on homogeneous spaces

Abstract

This paper studies reversibility and transitivity of semigroups acting on homogeneous spaces. Properties of the reversor set of a subsemigroup acting on homogeneous spaces are presented. Let G be a topological group and L a subgroup of G. Assume that S is a subsemigroup of G with nonempty interior. It is presented a study of the reversibility of the S-Action on <![CDATA[ $G/L$ ]]> in terms of the actions of S and L on homogeneous spaces of G. The results relate the reversibility and the transitivity of S in <![CDATA[ $G/L$ ]]> with the minimality of the action of L on homogeneous spaces of G. In addition, sufficient conditions for S to be right reversible in G if S is reversible in <![CDATA[ $G/L$ ]]> are presented.