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

All Science Journal Classification (ASJC) codes

  • Analysis

Fingerprint Dive into the research topics of 'Lattices of intermediate subfactors'. Together they form a unique fingerprint.

  • Cite this