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Hochschild DGLAs and torsion algebras

Lucian M. Ionescu
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Abstract

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.

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Lucian M. Ionescu. 1999-10-05. Hochschild DGLAs and torsion algebras. https://arxiv.org/abs/math/9910016

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