2014/01/10 by Michael Hartglass, Hartglass, Michael, David Penneys +1
Mathematics · Physics and Astronomy · #46L05 (Primary) #46L37 #46L54 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:46L05 #msc:46L37 #msc:46L54
paper · pdf · doi:10.48550/arxiv.1401.2485
47 pages, many figures
openalex publication_date 2014/01/10 · arxiv created 2014/01/11 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.