The embedding theorem for finite depth subfactor planar algebras

@article{Jones2010TheET,
  title={The embedding theorem for finite depth subfactor planar algebras},
  author={V. Jones and David Penneys},
  journal={arXiv: Operator Algebras},
  year={2010}
}
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. 
37 Citations

Figures from this paper

O A ] 1 0 N ov 2 01 6 ON FIXED POINT PLANAR ALGEBRAS by
  • 2016
On fixed point planar algebras
  • 2
  • PDF
Free analysis and planar algebras
  • 5
  • PDF
Affine modules and the Drinfeld Center
  • 4
  • PDF
A2-Planar Algebras I
  • 13
  • PDF
...
1
2
3
4
...

References

SHOWING 1-10 OF 29 REFERENCES
Skein theory for the D_2pi planar algebras
  • 59
  • PDF
Planar algebras, I
  • 236
  • PDF
Subfactors, Planar Algebras and Rotations
  • 16
  • PDF
On Jones' planar algebras
  • 34
  • Highly Influential
  • PDF
Quadratic Tangles in Planar Algebras
  • 57
  • PDF
Theory of operator algebras
  • 956
A Cyclic Approach to the Annular Temperley-Lieb Category
  • 5
  • PDF
...
1
2
3
...