Quadrilaterals of factors
by
Pinhas Grossman
Vanderbilt University
Coauthors: Masaki Izumi

An intermediate subfactor is an algebra P in between two factors: N ⊂ P ⊂ M, where N ⊂ M is an irreducible inclusion of factors with finite Jones index. For non-commuting pairs of intermediate subfactors, there is a rigidity to the inclusions which severely limits the number of possible configurations, in terms of the indices and the standard invariant of the total inclusion. In particular, there are exactly seven non-commuting quadrilaterals of factors whose sides have index less than or equal to 4. This is joint work with Masaki Izumi.

Date received: May 7, 2008