Stochastic Flow on the Quantum Heisenberg Manifold

Abstract

Following the work of Rieffel [1] on the deformation quantization of Heisenberg manifolds, a detailed study was undertaken in [2] to understand the geometry of such a manifold as a concrete example in non-commutative geometry [3]. In this article, a canonical non-commutative (quantum) stochastic flow is constructed on the quantum Heisenberg manifold which in a natural way is associated with the Dirac operator of the manifold.