Noncommutative Hamiltonian dynamics on foliated manifolds

Details Noncommutative Hamiltonian dynamics on foliated manifolds Noncommutative Hamiltonian dynamics on foliated manifolds

2009-12-10

arxiv.org/abs/0912.1923v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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