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

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.