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.


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