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An axiomatization of the lattice of higher relative commutants of a subfactor

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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 [Po5]| some criteria for bipartite graphs to be graphs of subfactors.

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Authors and Affiliations

  1. Departement of Mathematics, University of California, 90024, Los Angeles, CA, USA

    Sorin Popa

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  1. Sorin Popa
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Oblatum 25-XI-1994

Supported in part by NSF Grant DMS-9206984

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Popa, S. An axiomatization of the lattice of higher relative commutants of a subfactor. Invent Math 120, 427–445 (1995). https://doi.org/10.1007/BF01241137

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  • DOI: https://doi.org/10.1007/BF01241137

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