English

Partial actions of groups on quivers and path algebras

Representation Theory 2025-10-27 v1 Rings and Algebras

Abstract

In this article, we introduce the concept of partial actions of a group GG on quivers and demonstrate that for any given partial action of G on a quiver Γ\Gamma, there exists another quiver, Γ\Gamma' with a full GG-action. This is an enveloping action of the partial action of GG on Γ\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.

Keywords

Cite

@article{arxiv.2510.21035,
  title  = {Partial actions of groups on quivers and path algebras},
  author = {Wagner Cortes and Eduardo N. Marcos},
  journal= {arXiv preprint arXiv:2510.21035},
  year   = {2025}
}