1999/10/05 by Lucian M. Ionescu, Ionescu, Lucian M.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.DG #math.QA #msc:14A22 #msc:17A75 #msc:58A12
paper · pdf · doi:10.48550/arxiv.math/9910016
AMS-LaTex, 15 pages
arxiv created 1999/10/05 · arxiv updated 2009/11/30
The associator of a non-associative algebra is the curvature of the Hochschild quasi-complex. The relationship ``curvature-associator'' is investigated. Based on this generic example, we extend the geometric language of vector fields to a purely algebraic setting, similar to the context of Gerstenhaber algebras. We interprete the elements of a non-associative algebra with a Lie bracket as ``vector fields'' and the multiplication as a connection. We investigate conditions for the existance of an ``algebra of functions'' having as algebra of derivations the original non-associative algebra.