Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative Hamiltonian dynamics on foliated manifolds   First, we review the notion of a Poisson structure on a noncommutative
algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian
vector field on a noncommutative Poisson algebra. Then we describe a Poisson
structure on a noncommutative algebra associated with a transversely symplectic
foliation and construct a class of Hamiltonian vector fields associated with
this Poisson structure.

5
The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
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The categories of this paper are: cs
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat