2010
DOI: 10.1142/s0129167x10006380
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A Planar Algebra Construction of the Haagerup Subfactor

Abstract: Most known examples of subfactors occur in families, coming from algebraic objects such as groups, quantum groups and rational conformal field theories. The Haagerup subfactor is the smallest index finite-depth subfactor which does not occur in one of these families. In this paper we construct the planar algebra associated to the Haagerup subfactor, which provides a new proof of the existence of the Haagerup subfactor. Our technique is to find the Haagerup planar algebra as a singly generated subfactor planar … Show more

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Cited by 51 publications
(66 citation statements)
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“…We start with a loop γ on Γ of length 2n. If d(γ, Λ) > 1, we can use the 2-valent relation first considered in [Pet10,BPMS12] to fold γ inward by analyzing the capping action on 2-valent vertices as follows. We use the notation of [MP12a].…”
Section: -Valent Folding Relationmentioning
confidence: 99%
See 2 more Smart Citations
“…We start with a loop γ on Γ of length 2n. If d(γ, Λ) > 1, we can use the 2-valent relation first considered in [Pet10,BPMS12] to fold γ inward by analyzing the capping action on 2-valent vertices as follows. We use the notation of [MP12a].…”
Section: -Valent Folding Relationmentioning
confidence: 99%
“…These techniques have also been used to prove uniqueness results [BPMS12,Han10] and obstructions to possible principal graphs [Pet10,Mor13].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…The annular Temperley-Lieb category, especially the rotation, played an important role in the construction of certain exotic finite index subfactors [Pet10,BMPS09]. In a future paper with Jones, we will incorporate the odd Jones projections for infinite index (see [Bur03]) into the planar calculus, and we will give the analog of the annular Tempeley-Lieb category for infinite index.…”
Section: Future Researchmentioning
confidence: 99%
“…See [Wen90,MPS10,Pet10,BMPS12] for examples. A planar algebra S consists of vector spaces S n,± for n ∈ N ∪ {0}.…”
Section: Introductionmentioning
confidence: 99%