## The embedding theorem for finite depth subfactor planar algebras.(English)Zbl 1230.46055

Summary: We define a canonical planar $$\ast$$-algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional $$C^\ast$$-algebras with the Markov trace, we show that 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.

### MSC:

 46L37 Subfactors and their classification 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 57M20 Two-dimensional complexes (manifolds) (MSC2010)

### Keywords:

subfactors; planar algebras; Markov inclusion
Full Text:

### References:

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