{"paper":{"title":"Crossed products of operator algebras: applications of Takai duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Christopher Ramsey, Elias Katsoulis","submitted_at":"2017-05-24T12:44:02Z","abstract_excerpt":"Let $(\\mathcal G, \\Sigma)$ be an ordered abelian group with Haar measure $\\mu$, let $(\\mathcal A, \\mathcal G, \\alpha)$ be a dynamical system and let $\\mathcal A\\rtimes_{\\alpha} \\Sigma $ be the associated semicrossed product. Using Takai duality we establish a stable isomorphism \\[ \\mathcal A\\rtimes_{\\alpha} \\Sigma \\sim_{s} \\big(\\mathcal A \\otimes \\mathcal K(\\mathcal G, \\Sigma, \\mu)\\big)\\rtimes_{\\alpha\\otimes {\\rm Ad}\\: \\rho} \\mathcal G, \\] where $\\mathcal K(\\mathcal G, \\Sigma, \\mu)$ denotes the compact operators in the CSL algebra ${\\rm Alg}\\:\\mathcal L(\\mathcal G, \\Sigma, \\mu)$ and $\\rho$ den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08729","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"}