{"paper":{"title":"Cleft extensions of Koszul twisted Calabi-Yau algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fred van Oystaeyen, Xiaolan Yu, Yinhuo Zhang","submitted_at":"2014-05-23T12:35:01Z","abstract_excerpt":"Let $H$ be a twisted Calabi-Yau (CY) algebra and $\\sigma$ a 2-cocycle on $H$. Let $A$ be an $N$-Koszul twisted CY algebra such that $A$ is a graded $H^\\sigma$-module algebra. We show that the cleft extension $A#_\\sigma H$ is also a twisted CY algebra. This result has two consequences. Firstly, the smash product of an $N$-Koszul twisted CY algebra with a twisted CY Hopf algebra is still a twisted CY algebra. Secondly, the cleft objects of a twisted CY Hopf algebra are all twisted CY algebras. As an application of this property, we determine which cleft objects of $U(\\mathcal{D},\\lambda)$, a cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6040","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"}