An AF algebra associated with the Farey tessellation

Florin P. Boca

doi:10.4153/CJM-2008-043-1

An AF algebra associated with the Farey tessellation

Florin P. Boca

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We associate with the Farey tessellation of the upper half-plane an AF algebra U encoding the "cutting sequences" that define vertical geodesies. The Effros-Shen AF algebras arise as quotients of U. Using the path algebra model for AF algebras we construct, for each τ ∈ 0, 1/4 , projections (E_n) in U such that E_nE_n± ₁E_n ≤ τ E_n.

Original language	English (US)
Pages (from-to)	975-1000
Number of pages	26
Journal	Canadian Journal of Mathematics
Volume	60
Issue number	5
DOIs	https://doi.org/10.4153/CJM-2008-043-1
State	Published - Oct 2008

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General Mathematics

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An AF algebra associated with the Farey tessellation

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