Certain actions of finitely generated groups on higher dimensional noncommutative tori

2015/05/12 by Zhuofeng He, He, Zhuofeng
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1505.02968

openalex publication_date 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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