An axiomatization of the lattice of higher relative commutants of a subfactor. (English) Zbl 0831.46069

Summary: 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 sublattices and deduce from this and [the author, Ergodic Theory Dyn. Syst. 15, No. 5, 993-1003 (1995)] some criteria for bipartite graphs to be graphs of subfactors.


46L37 Subfactors and their classification
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