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

作者: Michael Hartglass , David Penneys

DOI: 10.1016/J.JFA.2014.08.024

关键词: Planar algebraSeries (mathematics)Algebra over a fieldMathematicsRank (linear algebra)Pure mathematicsFree probabilityTrace (linear algebra)

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

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