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arxiv: 1805.08971 · v2 · pith:G75WH3JJnew · submitted 2018-05-23 · 🧮 math.QA · math.CT· math.OA

Free oriented extensions of subfactor planar algebras

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keywords orientedplanarsubfactoralgebrasfreeadmitsextensionfactor
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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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