Cyclic Cohomology and Chern Connes pairing of some crossed product algebras

TL;DR

This paper computes cyclic and Hochschild cohomology groups and the Chern-Connes index for specific crossed product algebras involving quantum tori and finite cyclic groups.

Contribution

It provides explicit calculations of cohomology groups and index tables for these particular crossed product algebras, extending understanding of their geometric and algebraic properties.

Findings

Cyclic and Hochschild cohomology groups are explicitly computed.

Partial Chern-Connes index tables are established for each algebra.

Results enhance the understanding of noncommutative geometric invariants.

Abstract

We compute the cyclic and Hochschild cohomology groups for the algebras $\mathcal A_\theta^{alg} \rtimes \mathbb Z_3, \mathcal A_\theta^{alg} \rtimes \mathbb Z_4$ and $\mathcal A_\theta^{alg} \rtimes \mathbb Z_6$. We also compute the partial Chern-Connes index table for each of these algebras.