The cup subalgebra of a ${\rm II}_1$ factor given by a subfactor planar algebra is maximal amenable

Arnaud Brothier

Vol. 269 (2014), No. 1, 19–29

DOI: 10.2140/pjm.2014.269.19

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.

Keywords

planar algebra, von Neumann algebra, maximal abelian subalgebra, amenability

Mathematical Subject Classification 2010

Primary: 46L10

Secondary: 46K15

Milestones

Received: 17 October 2012

Revised: 3 May 2013

Accepted: 9 September 2013

Published: 15 July 2014