{"paper":{"title":"Deformation of Koszul algebras and the Duflo Isomorphism theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.KT","authors_text":"Murray Gerstenhaber","submitted_at":"2016-07-04T14:51:16Z","abstract_excerpt":"Let $\\mathfrak g$ be a finite dimensional Lie algebra over a field $\\mathbf k$, $U\\mathfrak g$ be its enveloping algebra and $S\\mathfrak g$ be the symmetric algebra on $\\mathfrak g$. Extending the work of Braverman and Gaitsgory on the deformation of Koszul algebras and the Poincar{\\'e}-Birkhoff-Witt theorem we obtain a generalized Duflo isomorphism which is valid also over fields of finite characteristic: $H_{\\text{Lie}}^n(\\mathfrak g, S\\mathfrak g) \\cong H_{\\text{Hoch}}^n(U\\mathfrak g,U\\mathfrak g)$ for all $n < \\operatorname{char}\\mathbf k$. This implies, in particular, that Duflo's classic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00917","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"}