The embedding theorem for finite depth subfactor planar algebras
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 July 2010
 DOI:
 10.48550/arXiv.1007.3173
 arXiv:
 arXiv:1007.3173
 Bibcode:
 2010arXiv1007.3173J
 Keywords:

 Mathematics  Operator Algebras;
 Mathematics  Quantum Algebra;
 46L37 (Primary);
 18D10;
 57M20 (Secondary)
 EPrint:
 30 pages, many figures