{"paper":{"title":"Twisted exterior derivatives for universal enveloping algebras I","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Zoran \\v{S}koda","submitted_at":"2008-06-05T14:24:17Z","abstract_excerpt":"Consider any representation $\\phi$ of a finite-dimensional Lie algebra $g$ by derivations of the completed symmetric algebra $\\hat{S}(g^*)$ of its dual. Consider the tensor product of $\\hat{S}(g^*)$ and the exterior algebra $\\Lambda(g)$. We show that the representation $\\phi$ extends canonically to the representation $\\tilde\\phi$ of that tensor product algebra. We construct an exterior derivative on that algebra, giving rise to a twisted version of the exterior differential calculus with the enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators betw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0978","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0806.0978/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}