# 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} }

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.

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