C$^*$-algebras from planar algebras I: Canonical C$^*$-algebras associated to a planar algebra
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- by Michael Hartglass and David Penneys PDF
- Trans. Amer. Math. Soc. 369 (2017), 3977-4019
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.References
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Additional Information
- Michael Hartglass
- Affiliation: Department of Mathematics, University of California, Riverside, Riverside, California 92521
- David Penneys
- Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90045-1555
- Address at time of publication: Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, Ohio 43210-1174
- MR Author ID: 942644
- Email: penneys.2@osu.edu
- Received by editor(s): June 9, 2014
- Received by editor(s) in revised form: May 31, 2015
- Published electronically: October 27, 2016
- © Copyright 2016 by the authors
- Journal: Trans. Amer. Math. Soc. 369 (2017), 3977-4019
- MSC (2010): Primary 46L05, 46L37; Secondary 46L54
- DOI: https://doi.org/10.1090/tran/6781
- MathSciNet review: 3624399