AF algebras in the quantum Gromov-Hausdorff propinquity space
Abstract
For unital AF algebras with faithful tracial states, we provide criteria for convergence in the quantum Gromov-Hausdorff propinquity. For any unital AF algebra, we introduce new Leibniz Lip-norms using quotient norms. Next, we show that any unital AF algebra is the limit of its defining inductive sequence of finite dimensional C*-algebras in quantum propinquity given any Lip-norm defined on the inductive sequence. We also establish sufficient conditions for when a *-isomorphism between two AF algebras produces a quantum isometry in the context of various Lip-norms.
Keywords
Cite
@article{arxiv.1612.02404,
title = {AF algebras in the quantum Gromov-Hausdorff propinquity space},
author = {Konrad Aguilar},
journal= {arXiv preprint arXiv:1612.02404},
year = {2017}
}
Comments
32 pages. Some clarifications made - especially in section 4. This article, in part, generalizes results from arXiv:1511.07114 and was originally part of arXiv:1608.07016v1, which was split due to length