Lattices of intermediate subfactors

Yasuo Watatani

    Research output: Contribution to journalArticlepeer-review

    26 Citations (Scopus)


    Let N be an irreducible subfactor of a type II1 factor M. If the Jones index [M: N] is finite, then the set L at(N ⊂ M) of the intermediate subfactors for the inclusion N ⊂ M forms a finite lattice. The commuting and co-commuting square conditions for intermediate subfactors are related to the modular identity in the lattice L at(N ⊂ N). In particular, simplicity of a finite group G is characterized in terms of commuting square conditions of intermediate subfactors for N ⊂ M = N ⋉ G. We investigate the question of which finite lattices can be realized as intermediate Subfactor lattices.

    Original languageEnglish
    Pages (from-to)312-334
    Number of pages23
    JournalJournal of Functional Analysis
    Issue number2
    Publication statusPublished - Sept 15 1996

    All Science Journal Classification (ASJC) codes

    • Analysis


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