Inductive limits of c*-algebras and compact quantum metric spaces

Konrad Aguilar*

*Kontaktforfatter for dette arbejde

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Given a unital inductive limit of C∗-algebras for which each C∗-algebra of the inductive sequence comes equipped with a Rieffel compact quantum metric, we produce sufficient conditions to build a compact quantum metric on the inductive limit from the quantum metrics on the inductive sequence by utilizing the completeness of the dual Gromov-Hausdorff propinquity of Latrémolière on compact quantum metric spaces. This allows us to place new quantum metrics on all unital approximately finite-dimensional (AF) algebras that extend our previous work with Latrémolière on unital AF algebras with faithful tracial state. As a consequence, we produce a continuous image of the entire Fell topology on the ideal space of any unital AF algebra in the dual Gromov-Hausdorff propinquity topology.

TidsskriftJournal of the Australian Mathematical Society
StatusE-pub ahead of print - 27. mar. 2020

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