The embedding theorem for finite depth subfactor planar algebras

Details The embedding theorem for finite depth subfactor planar algebras The embedding theorem for finite depth subfactor planar algebras

2010-07-19

arxiv.org/abs/1007.3173v1

Mathematics

Operator Algebras

30 pages, many figures

Scientific paper

We define a canonical relative commutant 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.

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