English

The embedding theorem for finite depth subfactor planar algebras

Operator Algebras 2010-07-20 v1 Quantum Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.1007.3173,
  title  = {The embedding theorem for finite depth subfactor planar algebras},
  author = {Vaughan F. R. Jones and David Penneys},
  journal= {arXiv preprint arXiv:1007.3173},
  year   = {2010}
}

Comments

30 pages, many figures

R2 v1 2026-06-21T15:49:51.466Z