2014/01/11 by Michael Hartglass, Hartglass, Michael, David Penneys +1
Mathematics · #46L09 (Primary) #46L37 #46L54 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:46L09 #msc:46L37 #msc:46L54
paper · pdf · doi:10.48550/arxiv.1401.2486
30 pages, many figures
arxiv created 2014/01/11 · arxiv updated 2014/01/14
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.