{"paper":{"title":"Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Fred van Oystaeyen, Jiwei He, Yinhuo Zhang","submitted_at":"2013-04-13T11:13:46Z","abstract_excerpt":"Let $A$ be a Koszul Artin-Schelter regular algebra with Nakayama automorphism $\\xi$. We show that the Yoneda Ext-algebra of the skew polynomial algebra $A[z;\\xi]$ is a trivial extension of a Frobenius algebra. Then we prove that $A[z;\\xi]$ is Calabi-Yau; and hence each Koszul Artin Schelter regular algebra is a subalgebra of a Koszul Calabi-Yau algebra. A superpotential $\\hat{w}$ is also constructed so that the Calabi-Yau algebra $A[z;\\xi]$ is isomorphic to the derivation quotient of $\\hat{w}$. The Calabi-Yau property of a skew polynomial algebra with coefficients in a PBW-deformation of a Kos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3799","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"}