Deformations of algebras over operads and Deligne's conjecture

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dc.creatorKontsevich, Maxim
dc.creatorSoibelman, Yan
dc.date2000-01-26
dc.date2000-01-27
dc.date.accessioned2026-07-07T04:33:26Z
dc.date.available2026-07-07T04:33:26Z
dc.descriptionIn present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces of deformations. We apply the general theory to the proof of Deligne's conjecture. The latter says that the Hochschild complex of an associative algebra carries a canonical structure of a dg-algebra over the chain operad of the little discs operad. In the course of the proof we construct an operad of geometric nature which acts on the Hochschild complex. It seems to be different from the brace operad (the latter was used in the previous approaches to the Deligne's conjecture). It follows from our results that the Grothendieck-Teichmüller group acts (homotopically) on the moduli space of structures of 2-algebras on the Hochschild complex. In the Appendix we develop a theory of piecewise algebraic chains and forms. It is suitable for real semialgebraic manifolds with corners (like Fulton-Macpherson compactifications of the configuration spaces of points).
dc.description67 pages, many figures, Abstract is modified
dc.identifierhttps://arxiv.org/abs/math/0001151
dc.identifierhttp://arxiv.org/abs/math/0001151
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58575
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.subjectCategory Theory
dc.subjectRings and Algebras
dc.subject18D50; 55P48; 16S80
dc.titleDeformations of algebras over operads and Deligne's conjecture
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