Lattices of intermediate subfactors

Yasuo Watatani

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

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
Volume140
Issue number2
DOIs
Publication statusPublished - Sep 15 1996

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Subfactors
Simplicity
Finite Group
Inclusion

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Lattices of intermediate subfactors. / Watatani, Yasuo.

In: Journal of Functional Analysis, Vol. 140, No. 2, 15.09.1996, p. 312-334.

Research output: Contribution to journalArticle

Watatani, Yasuo. / Lattices of intermediate subfactors. In: Journal of Functional Analysis. 1996 ; Vol. 140, No. 2. pp. 312-334.
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