On fixed point planar algebras
Abstract
To a weighted graph can be associated a bipartite graph planar algebra P. We construct and study the symmetric enveloping inclusion of P. We show that this construction is equivariant with respect to the automorphism group of P. The automorphism group of the weighted graph acts on P. We consider subgroups G of the automorphism group of the weighted graph such that the G-fixed point space P^G is a subfactor planar algebra. As an application we show that if G is amenable, then P^G is amenable as a subfactor planar algebra. We define the notions of a cocycle action of a Hecke pair on a tracial von Neumann algebra and the corresponding cross product. We show that a large class of symmetric enveloping inclusions of subfactor planar algebras can be described by such a cross product.
Cite
@article{arxiv.1603.01205,
title = {On fixed point planar algebras},
author = {Arnaud Brothier},
journal= {arXiv preprint arXiv:1603.01205},
year = {2016}
}
Comments
This paper replaces a previous version arXiv:1509.06654 entitled "Approximation properties for fixed point planar algebras" that contained a mistake