{"paper":{"title":"Simple Skew Category Algebras Associated with Minimal Partially Defined Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert, Patrik Lundstr\\\"om","submitted_at":"2012-05-07T20:35:01Z","abstract_excerpt":"In this article, we continue our study of category dynamical systems, that is functors $s$ from a category $G$ to $\\Top^{\\op}$, and their corresponding skew category algebras. Suppose that the spaces $s(e)$, for $e \\in \\ob(G)$, are compact Hausdorff. We show that if (i) the skew category algebra is simple, then (ii) $G$ is inverse connected, (iii) $s$ is minimal and (iv) $s$ is faithful. We also show that if $G$ is a locally abelian groupoid, then (i) is equivalent to (ii), (iii) and (iv). Thereby, we generalize results by \\\"{O}inert for skew group algebras to a large class of skew category al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1539","kind":"arxiv","version":1},"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"}