Subfactors of free products of rescalings of a II_1-factor

Details Subfactors of free products of rescalings of a II_1-factor Subfactors of free products of rescalings of a II_1-factor

2002-03-20

arxiv.org/abs/math/0203212v1

Mathematics

Operator Algebras

14 pages

Scientific paper

Let Q be any II_1-factor. It is shown that any standard lattice G can be realized as the standard invariant of a free product of (several) rescalings of Q. In particular, if Q has fundamental group equal to the positive reals and if P is the free product of infinitely many copies of Q, then P has subfactors giving rise to all possible standard invariants. Similarly, given a II_1-subfactor N of M, it is shown there is a subfactor R of S having the same standard invariant as N in M but where S, respectively R, is the free product of M, respectively N, with rescalings of Q.

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