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On deformation theory and graph homology

Fusun Akman·Lucian M. Ionescu·Papa A. Sissokho
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Abstract

Deformation theory of associative algebras and in particular of Poisson algebras is reviewed. The role of an almost contraction leading to a canonical solution of the corresponding Maurer-Cartan equation is noted. This role is reminiscent of the homotopical perturbation lemma, with the infinitesimal deformation cocycle as initiator. Applied to star-products, we show how Moyal's formula can be obtained using such an almost contraction and conjecture that the merger operation provides a canonical solution at least in the case of linear Poisson structures.

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Fusun Akman, Lucian M. Ionescu, Papa A. Sissokho. 2005-07-04. On deformation theory and graph homology. https://arxiv.org/abs/math/0507077

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