REFLECTORS AND GLOBALIZATIONS OF PARTIAL ACTIONS OF GROUPS

摘要

Given a partial action theta of a group on a set with an algebraic structure, we construct a reflector of theta in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In particular, if theta is a partial action on an algebra from a variety V, then we show that the problem reduces to the embeddability of a certain generalized amalgam of V-algebras associated with theta. As an application, we describe globalizable partial actions on semigroups, whose domains are ideals.