2011/04/12 by Johan Alm, Alm, Johan · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1104.2194
16 pages
arxiv created 2011/04/12 · openalex publication_date 2011/04/12 · arxiv updated 2011/04/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Using new configuration spaces, we give an explicit construction that extends Kontsevich's Lie-infinity quasi-isomorphism from polyvector fields to Hochschild cochains to a quasi-isomorphism of A-infinity algebras equipped with actions by homotopy derivations of the Lie algebra of polyvector fields. One may term this formality a formality of two-colored noncommutative Gerstenhaber homotopy algebras. In our result the action of polyvector fields by homotopy derivations of the wedge product on polyvector fields is not the adjoint action by the Schouten bracket, but a homotopy nontrivial and, in a sense, unique deformation of that action. As an application we give an explicit Duflo-type construction for Lie-infinity algebras that generalizes the Duflo-Kontsevich isomorphism between the Chevalley-Eilenberg cohomology of the symmetric algebra on a Lie algebra and the Chevalley-Eilenberg cohomology of the universal enveloping algebra of the Lie algebra.