The cup subalgebra has the absorbing amenability property

TL;DR

This paper proves that the cup subalgebra associated with any subfactor planar algebra possesses the absorbing amenability property, highlighting a significant structural feature in operator algebras.

Contribution

It establishes that the cup subalgebra has the absorbing amenability property for all subfactor planar algebras, a new structural result in von Neumann algebra theory.

Findings

Cup subalgebra has the absorbing amenability property

The property holds for all subfactor planar algebras

Advances understanding of subalgebra structures in von Neumann algebras

Abstract

Consider an inclusion of diffuse von Neumann algebras A c M . We say that A c M has the absorbing amenability property if for any diffuse subalgebra B c A and any amenable intermediate algebra B c D c M we have that D is contained in A. We prove that the cup subalgebra associated to any subfactor planar algebra has the absorbing amenability property.