Sorin Popa
An Axiomatization of the Lattice of Higher Relative Commutants of a Subfactor
The paper is published: Invent. Math. 120, 3 (1995) 427-445

MSC:

46L37 Subfactors and their classification

Abstract: We consider certain conditions for abstract lattices of commuting
squares, that we prove are necessary and sufficient for them to arise
as lattices of higher relative commutants of a subfactor. We call such
lattices standard and use this axiomatization to prove that their
sublattices are standard too. We consider a method for producing
sublatties and deduce from this and \cite {Po5} some criteria for
bipartite graphs to be graphs of subfactors.

Keywords: abstract lattices of commuting squares, bipartite graphs, graphs of subfactors