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

@article{Hartglass2014CalgebrasFP,
  title={C*-algebras from planar algebras I: Canonical C*-algebras associated to a planar algebra},
  author={Michael Hartglass and David Penneys},
  journal={Transactions of the American Mathematical Society},
  year={2014},
  volume={369},
  pages={3977-4019}
}
  • Michael Hartglass, David Penneys
  • Published 2014
  • Mathematics
  • Transactions of the American Mathematical Society
  • 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… CONTINUE READING

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