Masoud Khalkhali

Scalar curvature for the noncommutative two torus

We give a local expression for the {\it scalar curvature} of the noncommutative two torus

A New Cyclic Module for Hopf Algebras

A_{\theta} = C(\mathbb{T}_{\theta}^2)

Holomorphic Structures on the Quantum Projective Line

equipped with an arbitrary translation invariant complex structure and Weyl factor. This is achieved by evaluating the value of the (analytic continuation of the) {\it spectral zeta functional}

A NOTE ON CYCLIC DUALITY AND HOPF ALGEBRAS

\zeta_a(s): = \text{Trace}(a \triangle^{-s})

The homogeneous coordinate ring of the quantum projective plane

at

Noncommutative complex geometry of the quantum projective space

s=0

Weyl’s Law and Connes’ Trace Theorem for Noncommutative Two Tori

as a linear functional in

Curvature of the Determinant Line Bundle for the Noncommutative Two Torus

a \in C^{\infty}(\mathbb{T}_{\theta}^2)

Introduction to Hopf-Cyclic Cohomology

. A new, purely noncommutative, feature here is the appearance of the {\it modular automorphism group} from the theory of type III factors and quantum statistical mechanics in the final formula for the curvature. This formula coincides with the formula that was recently obtained independently by Connes and Moscovici in their recent paper.

A Riemann–Roch theorem for the noncommutative two torus

We define a new cyclic module, dual to the Connes-Moscovici cyclic module, for Hopf algebras, and give a characteristric map for the coaction of Hopf algebras. We also compute the resulting cyclic homology for cocommutative Hopf algebras, and some quantum groups.