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

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

2009-04-06

arxiv.org/abs/0904.0945v2

Proceedings de Algebraic and Geometric Deformation Spaces, Aspects of mathematics, Viewveg Verlag, 143-173. 2010

Mathematics

Quantum Algebra

31 pages, Added references, minor changes

Scientific paper

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.

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