{"paper":{"title":"Cocycle deformations for liftings of quantum linear spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Alessandro Ardizzoni, Claudia Menini, Margaret Beattie","submitted_at":"2010-11-02T15:48:20Z","abstract_excerpt":"Let $A$ be a Hopf algebra over a field $K$ of characteristic 0 and suppose there is a coalgebra projection $\\pi$ from $A$ to a sub-Hopf algebra $H$ that splits the inclusion. If the projection is $H$-bilinear, then $A$ is isomorphic to a biproduct $R #_{\\xi}H$ where $(R,\\xi)$ is called a pre-bialgebra with cocycle in the category $_{H}^{H}\\mathcal{YD}$. The cocycle $\\xi$ maps $R \\otimes R$ to $H$. Examples of this situation include the liftings of pointed Hopf algebras with abelian group of points $\\Gamma$ as classified by Andruskiewitsch and Schneider [AS1]. One asks when such an $A$ can be t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0648","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"}