Tensor Product Decompositions of II1 Factors Arising from Extensions of Amalgamated Free Product Groups

In this paper we introduce a new family of icc groups which satisfy the following product rigidity phenomenon, discovered in Drimbe etal. (J Reine Angew Math, 2016. arXiv:1611.02209): all tensor product decompositions of the II1 factor arise only from the canonical direct product decompositions of the underlying group . Our groups are assembled from certain HNN-extensions and amalgamated free products and 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.