On Deformations of Associative Algebras

dc.creatorBezrukavnikov, Roman
dc.creatorGinzburg, Victor
dc.date2005-03-03
dc.date2006-03-27
dc.date.accessioned2026-07-07T06:39:31Z
dc.date.available2026-07-07T06:39:31Z
dc.descriptionIn a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra A are controlled by the second Hochschild cohomology group of A. More generally, any n-parameter first order deformation of A gives, due to commutativity of the cup-product on Hochschild cohomology, a morphism from the graded algebra Sym(k^n) to Ext^*(A,A), the Ext-algebra in the category of A-bimodules. We prove that any extension of the n-parameter first order deformation of A to an INFINITE ORDER formal deformation provides a canonical `lift' of the graded algebra morphism above to a dg-algebra morphism from Sym(k^n) to the dg-algebra RHom(A,A), where the Symmetric algebra Sym(k^n) is viewed as a dg-algebra (generated by the vector space $\k^n$ placed in degree 2) with zero differential.
dc.descriptionA few comments added
dc.identifierhttps://arxiv.org/abs/math/0503053
dc.identifierhttp://arxiv.org/abs/math/0503053
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101106
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectK-Theory and Homology
dc.subjectRings and Algebras
dc.titleOn Deformations of Associative Algebras
dc.typetext

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