Rigid C^*-tensor categories of bimodules over interpolated free group factors
Operator Algebras
2015-06-11 v2 Category Theory
Quantum Algebra
Abstract
Given a countably generated rigid C^*-tensor category C, we construct a planar algebra P whose category of projections Pro is equivalent to C. From P, we use methods of Guionnet-Jones-Shlyakhtenko-Walker to construct a rigid C^*-tensor category Bim whose objects are bifinite bimodules over an interpolated free group factor, and we show Bim is equivalent to Pro. We use these constructions to show C is equivalent to a category of bifinite bimodules over L(F_infty).
Keywords
Cite
@article{arxiv.1208.5505,
title = {Rigid C^*-tensor categories of bimodules over interpolated free group factors},
author = {Arnaud Brothier and Michael Hartglass and David Penneys},
journal= {arXiv preprint arXiv:1208.5505},
year = {2015}
}
Comments
50 pages, many figures