{"paper":{"title":"Duality for Generalised Differentials on Quantum Groups and Hopf quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Shahn Majid, Wenqing Tao","submitted_at":"2012-07-30T17:24:46Z","abstract_excerpt":"We study generalised differential structures $\\Omega^1,d$ on an algebra $A$, where $A\\tens A\\to \\Omega^1$ given by $a\\tens b\\to a d b$ need not be surjective. The finite set case corresponds to quivers with embedded digraphs, the Hopf algebra left covariant case to pairs $(\\Lambda^1,\\omega)$ where $\\Lambda^1$ is a right module and $\\omega$ a right module map, and the Hopf algebra bicovariant case corresponds to morphisms $\\omega:A^+\\to \\Lambda^1$ in the category of right crossed (or Drinfeld-Radford-Yetter) modules over $A$. When $A=U(g)$ the generalised left-covariant differential structures "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7001","kind":"arxiv","version":3},"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"}