Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformation of algebroid bracket of differential forms and Poisson
  manifold   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.

30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci