C*-algebras from planar algebras I: Canonical C*-algebras associated to a planar algebra

Author:

Hartglass Michael,Penneys David

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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