An AF algebra associated with the Farey tessellation

Details An AF algebra associated with the Farey tessellation An AF algebra associated with the Farey tessellation

2005-11-21

arxiv.org/abs/math/0511505v6

Mathematics

Operator Algebras

23 pages, 20 figures

Scientific paper

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 $\tau \in (0,1/4\big]$, projections $(E_n)$
in this algebra such that $E_n E_{n\pm 1}E_n \leq \tau E_n$.

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