SUBFACTORS OF FREE PRODUCTS OF RESCALINGS OF A II_{1}-FACTOR

KEN DYKEMA

Abstract. Let Q be any II_{1}–factor. It is shown that any standard lattice 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 ⊂ M, it is shown there are subfactors N̂ ⊂ M̂ having the same standard invariant as N ⊂ M but where M̂, respectively N̂, is the free product of M, respectively N, with rescalings of Q.