Noncommutative Hamiltonian dynamics on foliated manifolds

Abstract

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.

13 pages

References in corpus (4)

• Lectures on Noncommutative Geometry
• The Egorov theorem for transverse Dirac type operators on foliated manifolds
• The trace formula for transversally elliptic operators on Riemannian foliations
• Noncommutative Poisson structures on Orbifolds