Journal article
W*-rigidity for the von Neumann algebras of products of hyperbolic groups
Geometric and Functional Analysis, Vol.26(1), pp.136-159
2016
DOI: 10.1007/s00039-016-0361-z
Abstract
We show that if Γ = Γ 1× ⋯ × Γ n is a product of n ≥ 2 non-elementary ICC hyperbolic groups then any discrete group Λ which is W∗-equivalent to Γ decomposes as a direct product of n ICC groups and does not decompose as a direct product of k ICC groups when n ≠ k. This gives a group-level strengthening of Ozawa and Popa’s unique prime decomposition theorem by removing all assumptions on the group Λ. This result in combination with Margulis’ normal subgroup theorem allows us to give examples of lattices in the same Lie group which do not generate stably equivalent II1 factors. © 2016, Springer International Publishing.
Details
- Title: Subtitle
- W*-rigidity for the von Neumann algebras of products of hyperbolic groups
- Creators
- I. Chifan - University of IowaR. de Santiago - University of IowaT. Sinclair - Purdue University West Lafayette
- Resource Type
- Journal article
- Publication Details
- Geometric and Functional Analysis, Vol.26(1), pp.136-159
- DOI
- 10.1007/s00039-016-0361-z
- ISSN
- 1016-443X
- Publisher
- Birkhauser Verlag AG
- Grant note
- Funding details: Directorate for Mathematical and Physical Sciences, MPS, 1301370
- Language
- English
- Date published
- 2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984230615202771
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