Free oriented extensions of subfactor planar algebras

Shamindra Kumar Ghosh; Corey Jones; B. Madhav Reddy

doi:10.1142/S0129167X18500933

Free oriented extensions of subfactor planar algebras

Shamindra Kumar Ghosh, Corey Jones, B. Madhav Reddy

Research output: Contribution to journal › Article › peer-review

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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 subfactor, the projection category of the free oriented extension admits a realization as bimodules of the hyperfinite II1 factor.

Original language	English
Article number	1850093
Journal	International Journal of Mathematics
Volume	29
Issue number	13
DOIs	https://doi.org/10.1142/S0129167X18500933
Publication status	Published - 1 Dec 2018

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title = "Free oriented extensions of subfactor planar 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 subfactor, the projection category of the free oriented extension admits a realization as bimodules of the hyperfinite II1 factor.",

keywords = "Subfactor planar algebras, adjoint functors, categories",

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AU - Ghosh, Shamindra Kumar

AU - Jones, Corey

AU - Reddy, B. Madhav

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N2 - 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 subfactor, the projection category of the free oriented extension admits a realization as bimodules of the hyperfinite II1 factor.

AB - 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 subfactor, the projection category of the free oriented extension admits a realization as bimodules of the hyperfinite II1 factor.

KW - Subfactor planar algebras

KW - adjoint functors

KW - categories

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U2 - 10.1142/S0129167X18500933

DO - 10.1142/S0129167X18500933

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JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 13

M1 - 1850093

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Free oriented extensions of subfactor planar algebras

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