# Free oriented extensions of subfactor planar algebras

@article{Ghosh2018FreeOE,
title={Free oriented extensions of subfactor planar algebras},
author={Shamindra Kumar Ghosh and Corey Jones and B Madhav Reddy},
journal={arXiv: Quantum Algebra},
year={2018},
pages={1850093}
}
• Published 2018
• Mathematics
• arXiv: Quantum Algebra
• 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 $\rm{II}_1$ subfactor, the projection category of the free oriented extension admits a realization as bimodules of the hyperfinite $\rm{II}_{1}$ factor.
3

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