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

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