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Popa, Sorin

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

Invent. Math. 120, No. 3, 427-445 (1995).
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.

Cited in 11 Reviews
Cited in 105 Documents

MSC:

46L37 Subfactors and their classification

Keywords:

abstract lattices of commuting squares; bipartite graphs; graphs of subfactors
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Full Text: DOI EuDML

References:

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[15] S. Popa: Classification of subfactors of type II. Acta Math.172 No. 2 (1994) 163-255 · Zbl 0853.46059 · doi:10.1007/BF02392646
[16] S. Popa: Classification of subfactors and of their endomorphisms. CBMS Lecture Notes Series, 1994
[17] S. Popa: Markov traces on universal Jones algebras and subfactors of finite index. Invent. Math.111 (1993) 375-405 · Zbl 0787.46047 · doi:10.1007/BF01231293
[18] S. Popa: Free independent sequences in typeII 1, factors and related problems (to appear in Asterisque)
[19] S. Popa: Some ergodic properties for infinite graphs associated to subfactors to appear in Ergod. Th. & Dynam. Sys.
[20] S. Popa: Symmetric enveloping algebras amenability and AFD properties for subfactors. Math, Research Letters1 (1994) 409-425 · Zbl 0902.46042
[21] F. Radulescu: Random matrices, amalgamated free products and subfactors of the von Neumann algebra of the free group. Invent. Math.115 (1994) 347-389 · Zbl 0861.46038 · doi:10.1007/BF01231764
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[23] S.Sunder:II 1 factors, their bimodules and hypergroups. Trans. Am. Math. Soc. (1993) · Zbl 0757.46053
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