The embedding theorem for finite depth subfactor planar algebras

By Vaughan F. R. Jones, David Penneys. 2010

54 citations recorded by the source corpus.

We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this planar algebra is isomorphic to the bipartite graph planar algebra of the Bratteli diagram of the inclusion. Finally, we show that a finite depth subfactor planar algebra is a planar subalgebra of the bipartite graph planar algebra of its principal graph.

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

View Paper: https://www.semanticscholar.org/paper/743157495dde3bddd82f2896ac1b8eb22d9ff86e

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. E. Peters
4. Stephen Bigelow
5. David Penneys
6. Vaughan F. R. Jones

In Geometry and Topology

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

In Mathematical Physics

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

Citations in the corpus

• Constructing the extended Haagerup planar algebra (2009, background): “The main reason for interest in graph planar algebras is the following result from [33] and [46].”