# Compact Quantum Metric Spaces from Free Graph Algebras

@inproceedings{Aguilar2021CompactQM, title={Compact Quantum Metric Spaces from Free Graph Algebras}, author={Konrad Aguilar and Michael Hartglass and David Penneys}, year={2021} }

Starting with a vertex-weighted pointed graph (Γ, μ, v0), we form the free loop algebra S0 defined in Hartglass-Penneys’ article on canonical C∗-algebras associated to a planar algebra. Under mild conditions, S0 is a non-nuclear simple C∗-algebra with unique tracial state. There is a canonical polynomial subalgebra A ⊂ S0 together with a Dirac number operator N such that (A,LA,N) is a spectral triple. We prove the Haagerup-type bound of Ozawa-Rieffel to verify (S0, A,N) yields a compact quantum…

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