The cup subalgebra has the absorbing amenability property

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.

5 pages, 5 figures, to appear in International Journal of Mathematics

References in corpus (3)

• Structure of $\mathrm{I}{\mathrm{I}}_1$ factors arising from free Bogoljubov actions of arbitrary groups
• The cup subalgebra of a II_1 factor given by a subfactor planar algebra is maximal amenable
• Maximal amenable subalgebras of von Neumann algebras associated with hyperbolic groups