Duke Mathematical Journal

Quadratic tangles in planar algebras

Vaughan F. R. Jones

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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.

Article information

Source
Duke Math. J., Volume 161, Number 12 (2012), 2257-2295.

Dates
First available in Project Euclid: 6 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1346936107

Digital Object Identifier
doi:10.1215/00127094-1723608

Mathematical Reviews number (MathSciNet)
MR2972458

Zentralblatt MATH identifier
1257.46033

Subjects
Primary: 46L37: Subfactors and their classification
Secondary: 18D50: Operads [See also 55P48] 16T99: None of the above, but in this section 57M27: Invariants of knots and 3-manifolds

Citation

Jones, Vaughan F. R. Quadratic tangles in planar algebras. Duke Math. J. 161 (2012), no. 12, 2257--2295. doi:10.1215/00127094-1723608. https://projecteuclid.org/euclid.dmj/1346936107


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