# The embedding theorem for finite depth subfactor planar algebras

### Vaughan F. R. Jones

UC, Berkeley, USA### David Penneys

UC, Berkeley, USA

## Abstract

We define a canonical 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.

## Cite this article

Vaughan F. R. Jones, David Penneys, The embedding theorem for finite depth subfactor planar algebras. Quantum Topol. 2 (2011), no. 3, pp. 301–337

DOI 10.4171/QT/23