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) |
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