2005/07/04 by Fusun Akman, Akman, Fusun, Lucian M. Ionescu +3
Mathematics · Physics and Astronomy · #52Dxx #58Hxx #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:52Dxx #msc:58Hxx
paper · pdf · doi:10.48550/arxiv.math/0507077
LaTeX, Elsevier style, 14 pages; submitted to Journal of Algebra 3/4/2005
arxiv created 2005/07/04 · arxiv updated 2009/12/01
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.