Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals
We introduce a topology on the ideal space of inductive limits of C*-algebras built by a topological inverse limit of the Fell topologies on the C*-algebras of the given inductive sequence and we produce conditions for when this topology agrees with the Fell topology of the inductive limit. With this topology, we impart criteria for when convergence of ideals of an AF algebra can provide convergence of quotients in the quantum Gromov-Hausdorff propinquity building off previous joint work with Latremoliere. These findings bestow a continuous map from a class of ideals of the Boca-Mundici AF algebra equipped with various topologies including Jacobson and Fell topologies to the space of quotients equipped with the propinquity topology.
- Pub Date:
- August 2016
- Mathematics - Operator Algebras;
- Mathematics - Functional Analysis;
- 58B34 (Primary)
- 42 pages. Sections 3 and 4 condensed into one section as stronger results were found that shortened many proofs. The article arXiv:1608.07016v1 was split into this current version and the new article arXiv:1612.02404 due to length