Tensor Product Decompositions of II1 Factors Arising from Extensions of Amalgamated Free Product Groups
Abstract
In this paper we introduce a new family of icc groups Γ 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(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.
- Publication:
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Communications in Mathematical Physics
- Pub Date:
- December 2018
- DOI:
- 10.1007/s00220-018-3175-z
- arXiv:
- arXiv:1710.05019
- Bibcode:
- 2018CMaPh.364.1163C
- Keywords:
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- Mathematics - Operator Algebras;
- Mathematics - Group Theory
- E-Print:
- doi:10.1007/s00220-018-3175-z