The homotopy Gerstenhaber algebra of Hochschild cochains of a regular algebra is formal

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dc.creatorDolgushev, Vasiliy
dc.creatorTamarkin, Dmitry
dc.creatorTsygan, Boris
dc.date2006-05-05
dc.date.accessioned2026-07-07T07:13:56Z
dc.date.available2026-07-07T07:13:56Z
dc.descriptionThe solution of Deligne's conjecture on Hochschild cochains and the formality of the operad of little disks provide us with a natural homotopy Gerstenhaber algebra structure on the Hochschild cochains of an associative algebra. In this paper we construct a natural chain of quasi-isomorphisms of homotopy Gerstenhaber algebras between the Hochschild cochain complex C(A) of a regular commutative algebra A over a field of characteristic zero and the Gerstenhaber algebra of multiderivations of A. Unlike the original approach of the second author based on the computation of obstructions our method allows us to avoid the bulky Gelfand-Fuchs trick and prove the formality of the homotopy Gerstenhaber algebra structure on the sheaf of polydifferential operators on a smooth algebraic variety, a complex manifold, and a smooth real manifold.
dc.description21 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0605141
dc.identifierhttp://arxiv.org/abs/math/0605141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112669
dc.subjectK-Theory and Homology
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleThe homotopy Gerstenhaber algebra of Hochschild cochains of a regular algebra is formal
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