English

Free oriented extensions of subfactor planar algebras

Quantum Algebra 2018-10-09 v2 Category Theory Operator Algebras

Abstract

We show that the restriction functor from oriented factor planar algebras to subfactor planar algebras admits a left adjoint, which we call the free oriented extension functor. We show that for any subfactor planar algebra realized as the standard invariant of a hyperfinite II1\rm{II}_1 subfactor, the projection category of the free oriented extension admits a realization as bimodules of the hyperfinite II1\rm{II}_{1} factor.

Keywords

Cite

@article{arxiv.1805.08971,
  title  = {Free oriented extensions of subfactor planar algebras},
  author = {Shamindra Kumar Ghosh and Corey Jones and B Madhav Reddy},
  journal= {arXiv preprint arXiv:1805.08971},
  year   = {2018}
}

Comments

29 pages, several figures, this version includes the complete statement and proof of universal property of free product of categories. We also re-defined projection category in terms of unitary Karaubi envelope and several other errors and typos are corrected. To appear in Int. J. Math

R2 v1 2026-06-23T02:05:14.312Z