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. 301–337DOI 10.4171/QT/23