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From a planar algebra, we give a functorial construction to produce numerousassociated $C^*$-algebras. Our main construction is a Hilbert $C^*$-bimodulewith 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-Robertsalgebras, Guionnet-Jones-Shlyakhtenko algebras, universal(Toeplitz-)Cuntz-Krieger algebras, and the newly introduced free graphalgebras. This is the first article in a series studying canonical$C^*$-algebras associated to a planar algebra.

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

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