2002/03/20 by Ken Dykema, Dykema, Ken
Mathematics · #46L37 #46L54 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #math.OA #msc:46L37 #msc:46L54
paper · pdf · doi:10.48550/arxiv.math/0203212
14 pages
arxiv created 2002/03/20 · openalex publication_date 2002/03/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Q be any II1-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 II1-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.