2017/10/31 by Ionuţ Chifan, Ionut Chifan, Rolando de Santiago +1 · 1 citation
Mathematics · #Direct product #Finite Group Theory Research #Free product #Geometric and Algebraic Topology #Graph #Homotopy and Cohomology in Algebraic Topology #Product (mathematics) #Tensor product #Tensor product of Hilbert spaces #Tensor product of algebras #math.GR #math.OA
paper · pdf · doi:10.1007/s00220-018-3175-z
openalex created_date 2017/11/10 · arxiv created 2017/11/28 · openalex publication_date 2018/06/12 · arxiv updated 2018/07/04 · openalex updated_date 2026/08/05
In this paper we introduce a new family of icc groups Γ which satisfy the following product rigidity phenomenon, discovered in [DHI16] (see also [dSP17]): all tensor product decompositions of the II1 factor L(Γ) arise only from the canonical direct product decompositions of the underlying group Γ. 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.