Solid von Neumann algebras

By Narutaka Ozawa. 2003

61 citations recorded by the source corpus.

We prove that the relative commutant of a diffuse von Neumann subalgebra in a hyperbolic group von Neumann algebra is always injective. It follows that any non-injective subfactor in a hyperbolic group von Neumann algebra is non-Gamma and prime. The proof is based on C*-algebra theory.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b610b94f2dc7297bd9e6ee079084d66345747599

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the superrigidity of malleable actions with spectral gap (2006, background): “compared with a result in [O2], showing that if � satisfies property AO and H is an abelian group, then the wreath product H ≀ � has the property AO as well. By [ O1 ] this implies L(� ⋉ H) = L ∞ ˆ”
On Ozawa's Property for Free Group Factors (2006, methodology): “C ∗ N (since α 1 is the ﬂip automorphism). But by (Corollary 4.3 in [P4]), this implies that vn = 0. Since τ(vnv∗ n) = τ(vv∗), it follows that v = 0, a contradiction.6 SORIN POPA §4. Remarks. 1◦. In ([O]) Ozawa called solid a II 1 factor N with all subalgebras with diﬀuse relative commutant being am”
A Kurosh-type theorem for type II1 factors (2004, methodology): “Now Lemma 5 in [ Oz2 ] can be interpreted as follows; Lemma 2.1 ([Oz2]).”
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, background): “On the other hand, Ozawa [84] verified the solidity of the group von Neumann algebras associated with hyperbolic groups.”
Some estimates for non-microstates free entropy dimension with applications to q-semicircular families (2003, background): “t W∗(X 1,...,Xn) embeds into the ultrapower of the hyperﬁnite II1 factor (i.e., X1,...,Xn have matricial microstates). 4. Ozawa’s condition and q-semicircularrandom variables. In his remarkable paper [8], Ozawa discusses the consequences of the following condition for a ﬁnite von Neumann algebra M. ”