An AF algebra associated with the Farey tessellation

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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 (En) in U such that EnEn± 1En ≤ τ En.

Original languageEnglish (US)
Pages (from-to)975-1000
Number of pages26
JournalCanadian Journal of Mathematics
Volume60
Issue number5
DOIs
StatePublished - Oct 2008

ASJC Scopus subject areas

  • Mathematics(all)

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