Formal deformations of Poisson structures in low dimensions

Details Formal deformations of Poisson structures in low dimensions Formal deformations of Poisson structures in low dimensions

2008-06-13

arxiv.org/abs/0806.2349v1

Pacific J. Math., 239 (2009), no. 1, 105--133

Mathematics

Quantum Algebra

27 pages

Scientific paper

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal deformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

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