C*-algebras from planar algebras II: The Guionnet-Jones-Shlyakhtenko C*-algebras

摘要

We study the C*-algebras arising in the construction of Guionnet-Jones-Shlyakhtenko (GJS) for a planar algebra. In particular, we show they are pairwise strongly Morita equivalent, we compute their K-groups, and we prove many properties, such as simplicity, unique trace, and stable rank 1. Interestingly, we see a K-theoretic obstruction to the GJS C*-algebra analog of Goldman-type theorems for II1-subfactors. This is the second article in a series studying canonical C*-algebras associated to a planar algebra. This is the published version of arXiv:1401.2486. (C) 2014 Elsevier Inc. All rights reserved.