An Af Algebra Associated with the Farey Tessellation
نویسنده
چکیده
To the Farey tessellation of the upper half-plane we associate an AF algebra A encoding the cutting sequences that define vertical geodesics. The Effros-Shen AF algebras arise as quotients of A. Using the path algebra model for AF algebras we construct, for each τ ∈ (0, 1 4 ], projections (En) in A such that EnEn±1En ≤ τEn.
منابع مشابه
An Af Algebra Associated with the Farey Tesselation
To the Farey tesselation of the upper half-plane we associate an AF algebra A encoding the ‘cutting sequences’ that define vertical geodesics. The Effros-Shen AF algebras arise as quotients of A. We define a unital completely positive map E : A → A and an endomorphism ρ : A→ A such that Eρ = idA , and which can be regarded as noncommutative analogs of the Farey map F : [0, 1] → [0, 1] acting on...
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