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arXiv · 1401.2485

$C^*$-algebras from planar algebras I: canonical $C^*$-algebras associated to a planar algebra

Michael Hartglass·David Penneys
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Abstract

From a planar algebra, we give a functorial construction to produce numerous associated $C^*$-algebras. Our main construction is a Hilbert $C^*$-bimodule with a canonical real subspace which produces Pimsner-Toeplitz, Cuntz-Pimsner, and generalized free semicircular $C^*$-algebras. By compressing this system, we obtain various canonical $C^*$-algebras, including Doplicher-Roberts algebras, Guionnet-Jones-Shlyakhtenko algebras, universal (Toeplitz-)Cuntz-Krieger algebras, and the newly introduced free graph algebras. This is the first article in a series studying canonical $C^*$-algebras associated to a planar algebra.

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Michael Hartglass, David Penneys. 2014-01-11. $C^*$-algebras from planar algebras I: canonical $C^*$-algebras associated to a planar algebra. https://arxiv.org/abs/1401.2485

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