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arXiv · 1807.01959

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

Alina Dobrogowska·Grzegorz Jakimowicz·Karolina Wojciechowicz
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Abstract

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

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Alina Dobrogowska, Grzegorz Jakimowicz, Karolina Wojciechowicz. 2018-07-05. Complete and vertical lifts of Poisson vector fields and infinitesimal deformations of Poisson tensor. https://arxiv.org/abs/1807.01959

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