English

An AF algebra associated with the Farey tessellation

Operator Algebras 2008-06-21 v6 Number Theory Quantum Algebra

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]\tau \in (0,1/4\big], projections (En)(E_n) in this algebra such that EnEn±1EnτEnE_n E_{n\pm 1}E_n \leq \tau E_n.

Keywords

Cite

@article{arxiv.math/0511505,
  title  = {An AF algebra associated with the Farey tessellation},
  author = {Florin P. Boca},
  journal= {arXiv preprint arXiv:math/0511505},
  year   = {2008}
}

Comments

23 pages, 20 figures

R2 v1 2026-07-22T17:27:41.229Z