Quantum ultrametrics on AF algebras and the Gromov-Hausdorff propinquity
Konrad Aguilar, Frédéric Latrémolière (2015)
Studia Mathematica
Similarity:
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite-dimensional C*-algebras for the quantum propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effrös-Shen AF algebras associated with continued fraction expansions of irrationals,...