On a class of II_1 factors with at most one Cartan subalgebra II
By Nathanial P. Brown Narutaka Ozawa, Sorin Popa. 2008
96 citations recorded by the source corpus.
This is a continuation of our previous paper studying the structure of Cartan subalgebras of von Neumann factors of type II_1. We provide more examples of II_1 factors having either zero, one or several Cartan subalgebras. We also prove a rigidity result for some group measure space II_1 factors.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/72613c88d450f5b5af9a47e8823d541c98eb660c
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In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
- Damien Gaboriau
- Y. Kida
- Adrian Ioana
- Russell Lyons
- Alexander Lubotzky
- Sorin Popa
- A. Furman
- Rostislav I. Grigorchuk
Citations in the corpus
- Proper actions of lamplighter groups associated with free groups (2007, unknown): “Theorem 1 has interesting consequences in view of a recent result of Ozawa and Popa [7].”
- Examples of factors which have no Cartan subalgebras (2012, unknown): “In the rigidity theory, Ozawa and Popa gave the first examples [24].”
- Group measure space decomposition of II1 factors and W*-superrigidity (2009, unknown): “nging to establish, and the only existing results cover very particular group actions: 1◦ profinite actions of products of free groups Γ = Fn1 ×···×Fn k , with k≥ 1, 2 ≤ ni≤ ∞ (see [OP07] and see also [OP08] for results covering a more general class of groups Γ); 2◦ profinite actions of non-trivial fr”
- Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors (2010, unknown): “Using ideas and techniques of [6, 19, 24, 27] and of the present paper, we obtain the following indecomposability results for free products of von Neumann algebras: Theorem 5.5.”
- Orbit Equivalence and Measured Group Theory (2010, background): “The (generalized) group-measure-space von Neumann algebra L ( R ) associated with R is generated by two families of operators of the separable Hilbert space L 2 ( R , ν ): There exist non-OE equivalence relations producing isomorphic L ( R ) ([CJ82], [OP08b]).”