Higher exchange relations

Shamindra Kumar Ghosh

Vol. 210 (2003), No. 2, 299–316

DOI: 10.2140/pjm.2003.210.299

Abstract

In this paper, we extend Landau’s notion of ‘exchange relations’ so as to make sense for arbitrary planar algebras, which need not necessarily be generated by its ‘2-boxes’. We show, as in Landau’s case, that these ‘higher exchange relation planar algebras’ are necessarily ‘finite dimensional’, and that examples of such planar algebras are given by all (even possibly reducible) depth two subfactors, as well as planar algebras associated to subfactors with principal graphs E₆ and E₈.

Milestones

Received: 18 January 2002

Revised: 4 July 2002

Published: 1 June 2003