45 citations · 323 across the 58 of their papers we have counts for
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The Ricci Curvature in Noncommutative Geometry
Remus Floricel, Asghar Ghorbanpour, Masoud Khalkhali
Motivated by the local formulae for asymptotic expansion of heat kernels in spectral geometry, we propose a definition of Ricci curvature in noncommutative settings. The Ricci oper…
A Scalar Curvature Formula For the Noncommutative 3-Torus
Masoud Khalkhali, Ali Moatadelro, Sajad Sadeghi
We compute the scalar curvature of a curved noncommutative 3-torus. To perturb the flat metric, the standard volume form on the noncommutative 3-torus is conformally perturbed and…
Monoidal Categories, 2-Traces, and Cyclic Cohomology
Mohammad Hassanzadeh, Masoud Khalkhali, Ilya Shapiro
In this paper we show that to a unital associative algebra object (resp. co-unital co-associative co-algebra object) of any abelian monoidal category endowed with a s…
On Logarithmic Sobolev Inequality for the Noncommutative Two Torus
Masoud Khalkhali, Sajad Sadeghi
An analogue of Gross' logarithmic Sobolev inequality for a class of elements of noncommutative two tori is proved.