Partial actions of groups on quivers and path algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915573715173376 |
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| author | Cortes, Wagner Marcos, Eduardo N. |
| author_facet | Cortes, Wagner Marcos, Eduardo N. |
| contents | 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 $Γ$, there exists another quiver, $Γ'$ with a full $G$-action. This is an enveloping action of the partial action of $G$ on $Γ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial actions of groups on quivers and path algebras Cortes, Wagner Marcos, Eduardo N. Representation Theory Rings and Algebras 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 $Γ$, there exists another quiver, $Γ'$ with a full $G$-action. This is an enveloping action of the partial action of $G$ on $Γ$. 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. |
| title | Partial actions of groups on quivers and path algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2510.21035 |