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

TL;DR

This paper proves that the cup subalgebra associated with a subfactor planar algebra within a II_1 factor is maximal amenable, utilizing Popa's approximative orthogonality property.

Contribution

It establishes the maximal amenability of the cup subalgebra in the context of subfactor planar algebras and II_1 factors, a novel result in operator algebra theory.

Findings

Cup subalgebra is maximal amenable

Utilizes Popa's approximative orthogonality property

Connects subfactor planar algebra with maximal amenability

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.