{"paper":{"title":"Skew group algebras of Jacobian algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Andrea Pasquali, Simone Giovannini","submitted_at":"2018-05-10T16:15:03Z","abstract_excerpt":"For a quiver with potential $(Q,W)$ with an action of a finite cyclic group $G$, we study the skew group algebra $\\Lambda G$ of the Jacobian algebra $\\Lambda = \\mathcal P(Q, W)$. By a result of Reiten and Riedtmann, the quiver $Q_G$ of a basic algebra $\\eta( \\Lambda G) \\eta$ Morita equivalent to $\\Lambda G$ is known. Under some assumptions on the action of $G$, we explicitly construct a potential $W_G$ on $Q_G$ such that $\\eta(\\Lambda G) \\eta\\cong \\mathcal P(Q_G , W_G)$. The original quiver with potential can then be recovered by the skew group algebra construction with a natural action of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04041","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}