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An AF algebra associated with the Farey tessellation

Florin P. Boca
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Abstract

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 $E_n E_{n\pm 1}E_n \leq τE_n$.

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Florin P. Boca. 2008-06-21. An AF algebra associated with the Farey tessellation. https://arxiv.org/abs/math/0511505

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