L∞-interpretation of a classification of deformations of Poisson structures in dimension three

Abstract

We give an L ∞-interpretation of the classification, obtained in [17], of the formal deformations of a family of exact Poisson structures in dimension three. We indeed reobtain the explicit formulas for all the formal deformations of these Poisson structures, together with a classification in the generic case, by constructing a suitable quasi-isomorphism between two L ∞-algebras, which are associated to these Poisson structures. © 2010 Vieweg+Teubner Verlag | GWV Fachverlage GmbH, Wiesbaden.