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Stochastic Flow on the Quantum Heisenberg Manifold

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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.

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References

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    M. Rieffel : Deformation quantization of Heisenberg manifolds, Commun. Math. Phys. 122, 531–562 (1989).MathSciNetCrossRefzbMATHGoogle Scholar
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    P. S. Chakraborty and Kalyan B. Sinha : Geometry on the quantum Heisenberg manifold, Journal of Functional analysis, 203, 425–452 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
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    Kalyan B. Sinha and Debashish Goswami: “Quantum Stochastic Processes and Non-Commutative Geometry”, Cambridge Tracts in Mathematics # 169, Cambridge University Press, U.K. 2007.CrossRefzbMATHGoogle Scholar

Copyright information

© Hindustan Book Agency 2007

Authors and Affiliations

  1. 1.Indian Statistical InstituteDelhi CentreNew DelhiIndia

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