Bass-Serre rigidity results in von Neumann algebras
By I. Chifan, Cyril Houdayer. 2008
78 citations recorded by the source corpus.
We obtain new Bass-Serre type rigidity results for ${\rm II_1}$ equivalence relations and their von Neumann algebras, coming from free ergodic actions of free products of groups on the standard probability space. As an application, we show that any non-amenable factor arising as an amalgamated free product of von Neumann algebras $\mathcal{M}_1 \ast_B \mathcal{M}_2$ over an abelian von Neumann algebra $B$, is prime, i.e. cannot be written as a tensor product of diffuse factors. This gives, both in the type ${\rm II_1}$ and in the type ${\rm III}$ case, new examples of prime factors.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ae026b66310dd3c9b14bc737817f9c3f2eb7eea1
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In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors (2010, methodology): “Intertwining techniques for semifinite von Neumann algebras were developed in [6].”
- Type III factors with unique Cartan decomposition (2012, methodology): “ble deformation (in the sense of [Po03, Po06c]) for such an amalgamated free product. A combination of this malleable deformation and the spectral gap rigidity methods of [Po06a, Po06b], then lead in [CH08] to a general primeness result for amalgamated free product von Neumann algebras M= M1 ∗BM2 ov”