✦ LIBER ✦

Lattices of Intermediate Subfactors

✍ Scribed by Yasuo Watatani

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 807 KB
Volume: 140
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.0110

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✦ Synopsis

Let N be an irreducible subfactor of a type II 1 factor M. If the Jones index [M : N] is finite, then the set Lat(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 Lat(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.

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