Hochschild and cyclic homology of the crossed product of algebraic irrational rotational algebra by finite subgroups of \({SL}(2,\mathbb{Z})\) (Q897766)

The author considers a crossed product of the algebraic non-commutative torus by the finite groups \(\mathbf{Z}_2, \mathbf{Z}_3, \mathbf{Z}_4\) and \(\mathbf{Z}_6\) acting on the generators of the torus. It is shown that the even cyclic homology group is isomorphic to \(\mathbf{C}^6, \mathbf{C}^8, \mathbf{C}^9\) and \( \mathbf{C}^{10}\), respectively. The Hochschild cohomology groups are shown to be trivial unless \(n=0\) in which case they are \(\mathbf{C}^5, \mathbf{C}^7, \mathbf{C}^8 \) and \( \mathbf{C}^9\), respectively. A draft of the paper is available at \texttt{http://arxiv.org/abs/1403.5983}.