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

Abstract

Let $\Gamma \subset SL(2,\mathbb{Z})$ be a finite subgroup acting on the irrational rotational algebra ${\mathcal{A}}_{\theta }$ via the restriction of the canonical action of $SL(2,\mathbb{Z})$. Consider the crossed product algebra ${\mathcal{A}}_{\theta }^{alg}⋊\Gamma$ obtained by the restriction of the $\Gamma$ action on the algberaic irrational rotational algebra. In this paper we prove many results on the homology group of the crossed product algebra ${\mathcal{A}}_{\theta }^{alg}⋊\Gamma$. We also analyse the case of the smooth crossed product algebra, ${\mathcal{A}}_{\theta }⋊\Gamma$ and calculate some of its homology groups.

References in corpus (2)

• The structure of crossed products of irrational rotation algebras by finite subgroups of SL_2 (Z)
• K-theory of noncommutative Bieberbach manifolds

Cited by in corpus (3)

• Hochschild and Cyclic Homology of Quantum Kummer Spaces
• Non-commutative Poisson Structures on quantum torus orbifolds
• Equivariant Cartan Homotopy Formulae for $DG$-Algebra