An AF algebra associated with the Farey tessellation

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To the Farey tessellation of the upper half-plane we associate an AF algebra encoding the cutting sequences that define vertical geodesics. The Effros-Shen AF algebras arise as quotients of our algebra. Using the path algebra model for AF algebras we construct for each $τ\in (0,1/4\big]$, projections $(E_n)$ in this algebra such that $E_n E_{n\pm 1}E_n \leq τE_n$.
23 pages, 20 figures

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Operator Algebras, Number Theory, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/163278

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511505
 http://arxiv.org/abs/math/0511505

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arXiv