On automorphisms of monotone transformation posemigroups

Abstract

In this paper, we provide a simple generalization of results of Sullivan for [Formula: see text] the full transformation monotone pomonoid and for [Formula: see text] the partial transformation monotone pomonoid by showing that every automorphism of [Formula: see text] and [Formula: see text] is inner induced by the elements of [Formula: see text] the pogroup of all ordered bijections on [Formula: see text]. We also show that [Formula: see text] is isomorphic to [Formula: see text]. Finally, we apply these results to get some more results in this direction.