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Certain actions of finitely generated groups on higher dimensional noncommutative tori (1505.02968v1)
Published 12 May 2015 in math.OA
Abstract: We study certain actions of finitely generated abelian groups on higher dimensional noncommutative tori. Given a dimension $d$ and a finitely generated abelian group $G$, we apply a certain function to detect whether there is a simple noncommutative $d$-torus which admits a specific action by $G$. We also describe the condition of $G$ under which the associated crossed product is an AF algebra.