Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor

Alina Dobrogowska; Grzegorz Jakimowicz; Karolina Wojciechowicz

paper

Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor

arXiv:1807.01959

Abstract

In this paper we prove that both complete and vertical lifts of a Poisson vector field from a Poisson manifold $(M, π)$ to its tangent bundle $(T M, π_{T M})$ are also Poisson. We use this fact to describe the infinitesimal deformations of Poisson tensor $π_{T M}$ . We study some of their properties and present a extensive set of examples in a low dimensional case.

24 pages