Geodesic
An AF Algebra Associated with the Farey Tessellation
Canadian journal of mathematics, Tome 60 (2008) no. 5, pp. 975-1000

Voir la notice de l'article provenant de la source Cambridge University Press

We associate with the Farey tessellation of the upper half-plane an $\text{AF}$ algebra $\mathfrak{A}$ encoding the “cutting sequences” that define vertical geodesics. The Effros–Shen $\text{AF}$ algebras arise as quotients of $\mathfrak{A}$ . Using the path algebra model for $\text{AF}$ algebras we construct, for each $\tau \,\,\in \,\,\left( 0 \right.,\left. \frac{1}{4} \right]$ , projections $({{E}_{n}})$ in $\mathfrak{A}$ such that ${{E}_{n}}{{E}_{n\pm 1}}E\le \tau {{E}_{n}}$ .
DOI : 10.4153/CJM-2008-043-1
Mots-clés : 46L05, 11A55, 11B57, 46L55, 37E05, 82B20 
Boca, Florin P. An AF Algebra Associated with the Farey Tessellation. Canadian journal of mathematics, Tome 60 (2008) no. 5, pp. 975-1000. doi: 10.4153/CJM-2008-043-1
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