AF algebras in the quantum Gromov-Hausdorff propinquity space

2016/12/07 by Konrad Aguilar, Aguilar, Konrad
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1612.02404

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.

Cited by

• Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals

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