Partial actions of groups on quivers and path algebras

Abstract

In this article, we introduce the concept of partial actions of a group $G$ on quivers and demonstrate that for any given partial action of G on a quiver $\Gamma$, there exists another quiver, ${\Gamma }^{\prime }$ with a full $G$-action. This is an enveloping action of the partial action of $G$ on $\Gamma$. We also introduce partial actions of groups on algebras by subalgebras instead of ideals and we define enveloping actions in this case. We show that any partial action of a group on a path algebra that is induced by a partial action on a quiver has an enveloping action.