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Communications in Mathematical Physics

, Volume 364, Issue 3, pp 1163–1194 | Cite as

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

  • Ionut Chifan
  • Rolando de Santiago
  • Wanchalerm Sucpikarnon
Article
  • 36 Downloads

Abstract

In this paper we introduce a new family of icc groups \({\Gamma}\) which satisfy the following product rigidity phenomenon, discovered in Drimbe et al. (J Reine Angew Math, 2016. arXiv:1611.02209): all tensor product decompositions of the II1 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.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe University of IowaIowa CityUSA
  2. 2.Department of MathematicsUniversity of California Los AngelesLos AngelesUSA

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