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 subfactor, the projection category of the free oriented extension admits a realization as bimodules of the hyperfinite factor.
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