{"paper":{"title":"Skew Category Algebras Associated with Partially Defined Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert, Patrik Lundstr\\\"om","submitted_at":"2010-06-24T12:39:14Z","abstract_excerpt":"We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor $s$ from a category $G$ to $\\Top^{\\op}$ and show that it defines what we call a skew category algebra $A \\rtimes^{\\sigma} G$. We study the connection between topological freeness of $s$ and, on the one hand, ideal properties of $A \\rtimes^{\\sigma} G$ and, on the other hand, maximal commutativity of $A$ in $A \\rtimes^{\\sigma} G$. In particular, we show that if $G$ is a groupoid and for each $e \\in \\ob(G)$ the group of all morphisms $e \\rightarrow e$ is countable and the to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4776","kind":"arxiv","version":2},"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"}