An AF algebra associated with the Farey tessellation
Florin P. Boca
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∈ (0,1/4], projections (En) in this algebra such that En En 1En ≤ τEn.
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