The cup subalgebra of a II_1 factor given by a subfactor planar algebra is maximal amenable

Abstract

To every subfactor planar algebra was associated a II_1 factor with a canonical abelian subalgebra generated by the cup tangle. Using Popa's approximative orthogonality property, we show that this cup subalgebra is maximal amenable.

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• Rigid C^*-tensor categories of bimodules over interpolated free group factors
• A class of $\mathrm{I}{\mathrm{I}}_1$ factors with an exotic abelian maximal amenable subalgebra
• Maximal injective and mixing masas in group factors

Cited by in corpus (5)

• 1-bounded entropy and regularity problems in von Neumann algebras
• Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups
• A random matrix approach to absorption in free products
• The cup subalgebra has the absorbing amenability property
• Maximal amenability of the generator subalgebra in $q$-Gaussian von Neumann algebras