Quadratic Tangles in Planar Algebras

Abstract

In planar algebras, we show how to project certain simple "quadratic" tangles onto the linear space spanned by "linear" and "constant" tangles. We obtain some corollaries about the principal graphs and annular structure of subfactors.

References in corpus (3)

• Subfactors of index less than 5, part 2: triple points
• Subfactors of index less than 5, part 1: the principal graph odometer
• Knot polynomial identities and quantum group coincidences

Cited by in corpus (14)

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• Planar Para Algebras, Reflection Positivity
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• 2-supertransitive subfactors at index $3+\sqrt{5}$
• Drinfeld center of planar algebra
• Calculating two-strand jellyfish relations
• Constructing spoke subfactors using the jellyfish algorithm
• An obstruction to subfactor principal graphs from the graph planar algebra embedding theorem
• A rotational approach to triple point obstructions
• Subfactors of index exactly 5
• Realizations of Rigid C*-Tensor Categories as Bimodules over GJS C*-Algebras
• The planar parafermion algebra: The ${\mathbb{Z}}_N$ clock model and the coupled Temperley-Lieb algebra