On deformation of associative algebras and graph homology |
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Authors: | Fusun Akman Lucian M Ionescu Papa Sissokho |
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Institution: | aDepartment of Mathematics, Illinois State University, IL 61790-4520, USA |
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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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Keywords: | Deformation theory Star-product Graph homology |
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