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Search: MSC category 11B57 ( Farey sequences; the sequences ${1^k, 2^k, \cdots}$ )

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1. CJM 2008 (vol 60 pp. 975)

Boca, Florin P.
An AF Algebra Associated with the Farey Tessellation
We associate with the Farey tessellation of the upper half-plane an AF algebra $\AA$ encoding the ``cutting sequences'' that define vertical geodesics. The Effros--Shen AF algebras arise as quotients of $\AA$. Using the path algebra model for AF algebras we construct, for each $\tau \in \big(0,\frac{1}{4}\big]$, projections $(E_n)$ in $\AA$ such that $E_n E_{n\pm 1}E_n \leq \tau E_n$.

Categories:46L05, 11A55, 11B57, 46L55, 37E05, 82B20

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