Quadratic Tangles in Planar Algebras

By Vaughan F. R. Jones. 2010

67 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bed26764351cd7daa4928c0c6e5f834327509d14

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Noah Snyder
2. S. Morrison
3. David Penneys
4. E. Peters
5. Zhengwei Liu
6. Vaughan F. R. Jones
7. T. Banica

In Geometry and Topology

1. Zhengwei Liu
2. Noah Snyder
3. S. Morrison
4. Vaughan F. R. Jones
5. David Penneys
6. E. Peters
7. David E. V. Rose
8. Bob Coecke

In Mathematical Physics

1. Zhengwei Liu
2. Noah Snyder
3. S. Morrison
4. Vaughan F. R. Jones
5. David Penneys
6. E. Peters
7. David E. V. Rose
8. Bob Coecke

Citations in the corpus

• Skein theory for the D_2pi planar algebras (2008, methodology): “Using the techniques in [25] and [30], find the generator and some of the relations for this planar algebra.”
• Exchange relation planar algebras of small rank (2013, background): “We refer the reader to [22] for the definition of subfactor planar algebras.”
• The embedding theorem for finite depth subfactor planar algebras (2010, methodology): “We use the definition of [11] (see also [17]), but we do not reproduce it here.”