Journal of Operator Theory

Volume 49, Issue 1, Winter 2003 pp. 185-201.

Probability and geometry on some noncommutative manifolds

Authors: P.S. Chakraborty, (1) D. Goswami, (2) and K.B. Sinha (3)
Author institution: (1) Statistics and Mathematical Division, Indian Statistical Institute, 7, S. J. S. S. Marg, New Delhi-110016, India
(2) Statistics and Mathematics Division, Indian Statistical Institute, Kolkata Centre, 203, B.T. Road, Kolkata 700 108, India
(3) Statistics and Mathematical Division, Indian Statistical Institute, 7, S. J. S. S. Marg, New Delhi-110016, India

Summary: In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl $C^*$-algebra, the Laplacian associated with a natural stochastic process is obtained and associated volume form is calculated.

Keywords: Noncommutative torus, Laplacian, Dixmier trace, quantum stochastic process

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