Hochschild and cyclic homology of the crossed product of algebraic irrational rotational algebra by finite subgroups of

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• 作者：Safdar Quddus ^{safdar@niser.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：58B34 ; 19D55
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：447
• 期：Complete
• 页码：322-366
• 全文大小：590 K

文摘

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