Cohomology of ${\mathcal{A}}_{\theta }^{alg}⋊{\mathbb{Z}}_2$ and its Chern-Connes pairing

Abstract

We calculate the Hochschild and cyclic cohomology of the ${\mathbb{Z}}_2$ toroidal orbifold ${\mathcal{A}}_{\theta }^{alg}⋊{\mathbb{Z}}_2$. We also calculate the Chern-Connes pairing of the even cyclic cohomology group with the known elements of $K_0({\mathcal{A}}_{\theta }^{alg}⋊{\mathbb{Z}}_2)$.

arXiv commentFinal version to appear in Journal of Noncommutative Geometry