Reflectors and globalizations of partial actions of groups

Abstract: 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 ${\sf V}$, then we show that the problem reduces to the embeddability of certain generalized amalgam of ${\sf V}$-algebras associated with $\theta$. As an application, we describe globalizable partial actions on semigroups, whose domains are ideals.