On deformation theory and graph homology
Quantum Algebra
2007-05-23 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0507077,
title = {On deformation theory and graph homology},
author = {Fusun Akman and Lucian M. Ionescu and Papa A. Sissokho},
journal= {arXiv preprint arXiv:math/0507077},
year = {2007}
}
Comments
LaTeX, Elsevier style, 14 pages; submitted to Journal of Algebra 3/4/2005