Reflectors and globalizations of partial actions of groups

2016/02/17 by Khrypchenko, Mykola, Novikov, Boris · 1 citation
#Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1602.05504

Abstract

Given a partial action θ of a group on a set with an algebraic structure, we construct a reflector of θ in the corresponding subcategory of global actions and study the question when this reflector is a globalization. In particular, if θ 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 θ. As an application, we describe globalizable partial actions on semigroups, whose domains are ideals.

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