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arXiv · 1806.08142

Deformation of algebroid bracket of differential forms and Poisson manifold

Alina Dobrogowska·Grzegorz Jakimowicz·Karolina Wojciechowicz
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Abstract

We construct the family of algebroid brackets $[\cdot,\cdot]_{c,v}$ on the tangent bundle $T^*M$ to a Poisson manifold $(M,\pi)$ starting from an algebroid bracket of differential forms. We use these brackets to generate Poisson structures on the tangent bundle $TM$. Next, in the case when $M$ is equipped with a bi-Hamiltonian structure $(M,\pi_1, \pi_2)$ we show how to construct another family of Poisson structures. Moreover we present how to find Casimir functions for those structures and we discuss some particular examples.

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Alina Dobrogowska, Grzegorz Jakimowicz, Karolina Wojciechowicz. 2018-06-21. Deformation of algebroid bracket of differential forms and Poisson manifold. https://arxiv.org/abs/1806.08142

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