English

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