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- Title
Rigidity for Von Neumann Algebras Given by Locally Compact Groups and Their Crossed Products.
- Authors
Brothier, Arnaud; Deprez, Tobe; Vaes, Stefaan
- Abstract
We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected simple Lie groups of real rank one, the crossed product has a unique Cartan subalgebra up to unitary conjugacy. We then deduce a W* strong rigidity theorem for irreducible actions of products of such groups. More generally, our results hold for products of locally compact groups that are nonamenable, weakly amenable and that belong to Ozawa’s class S<inline-graphic></inline-graphic>.
- Subjects
VON Neumann algebras; COMPACT groups; CROSSED products of algebras; FREE probability theory; LIE groups
- Publication
Communications in Mathematical Physics, 2018, Vol 361, Issue 1, p81
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-018-3091-2