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arXiv · 1612.02404

AF algebras in the quantum Gromov-Hausdorff propinquity space

Konrad Aguilar
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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.

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Konrad Aguilar. 2016-12-07. AF algebras in the quantum Gromov-Hausdorff propinquity space. https://arxiv.org/abs/1612.02404

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