Cuntz-Li algebras from a-adic numbers

S. Kaliszewski; Tron Omland; John Quigg

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arXiv · 1211.4806

Cuntz-Li algebras from a-adic numbers

S. Kaliszewski·Tron Omland·John Quigg

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Abstract

The a-adic numbers are those groups that arise as Hausdorff completions of noncyclic subgroups of the rational numbers. We give a crossed product construction of (stabilized) Cuntz-Li algebras coming from the a-adic numbers and investigate the structure of the associated algebras. In particular, these algebras are in many cases Kirchberg algebras in the UCT class. Moreover, we prove an a-adic duality theorem, which links a Cuntz-Li algebra with a corresponding dynamical system on the real numbers. The paper also contains an appendix where a nonabelian version of the "subgroup of dual group theorem" is given in the setting of coactions.

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BibTeX RIS

S. Kaliszewski, Tron Omland, John Quigg. 2012-11-20. Cuntz-Li algebras from a-adic numbers. https://arxiv.org/abs/1211.4806

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