April 20, 2018

Tensor Product Decompositions f II1 Factors Arising From Amalgamated Free Product Groups

We show that a large collection of icc groups G give rise to II1 factors which satisfy the following product rigidity phenomenon: all tensor product decompositions of the group von Neumann algebra L(G) must arise from canonical direct product decomposition of the underlying group G. This collection of groups include many remarkable groups studied throughout mathematics such as graph product groups, poly-amalgam groups, Burger-Mozes groups, Higman group, various integral two-dimensional Cremona groups, etc. As a consequence, we obtain several new examples of groups that give rise to prime factors.