Tensor product decompositions of II${}_1$ factors arising from extensions of amalgamated free product groups

Abstract

In this paper we introduce a new family of icc groups $\Gamma$ which satisfy the following product rigidity phenomenon, discovered in [DHI16] (see also [dSP17]): all tensor product decompositions of the II${}_1$ factor $L(\Gamma )$ arise only from the canonical direct product decompositions of the underlying group $\Gamma$. 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.

References in corpus (3)

• Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)
• Unbounded derivations, free dilations and indecomposability results for II${}_1$ factors
• Global well-posedness of the two-dimensional exterior Navier-Stokes equations for non-decaying data

Cited by in corpus (3)

• Some Applications of Group Theoretic Rips Constructions to the Classification of von Neumann Algebras
• Orbit equivalence rigidity for product actions
• Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms