$L_{\infty }$-interpretation of a classification of deformations of Poisson structures in dimension three

Abstract

We give an $L_{\infty }$-interpretation of the classification, obtained in [AP2], of the formal deformations of a family of exact Poisson structures in dimension three. We indeed obtain again 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 $L_{\infty }$-algebras, which are associated to these Poisson structures.

31 pages, Added references, minor changes