A Kurosh-type theorem for type II1 factors
By Nathanial P. Brown Narutaka Ozawa. 2004
133 citations recorded by the source corpus.
We prove a Kurosh type theorem for free-product type II_1 factors. In particular, if M = LF_2 \otimes R, then the free-product type II_1 factors M*...*M are all prime and pairwise non-isomorphic. This paper is a continuation of [N. Ozawa, Solid von Neumann algebras] and [N. Ozawa and S. Popa, Some prime factorization results for type II_1 factors].
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4513690da12aa3f5491eaf24da184cf8759352e5
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In Geometry and Topology
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Citations in the corpus
- On the superrigidity of malleable actions with spectral gap (2006, background): “es of prime factors. Lemma 5.2 allows deriving new examples of prime II1 factors, i.e. factors M that cannot be decomposed as a tensor products 22 SORIN POPA M = Q⊗Q0 with Q,Q0 II1 factors (see [O1], [O2], [Pe] for other examples of such factors): Theorem. Let Λ be an arbitrary non-amenable group an”
- Bass-Serre rigidity results in von Neumann algebras (2008, background): “Results of this type have been first obtained by Ozawa in his pioneering paper [24] for plain free products M = M1 ∗M2 of semi-exact II1 factors.”
- A CLASS OF SUPERRIGID GROUP VON NEUMANN ALGEBRAS (2010, background): “(3) The subtlety of how LG depends on G is nicely illustrated by the following remark due to Ozawa [Oza06].”
- A SURVEY OF MEASURED GROUP THEORY (2009, background): “Sauer and Thom [107] develop new homological tools (including a spectral sequence for associated to strongly normal subrelations) to study l2-Betti numbers for groups, relations and measured groupoids.”
- Amalgamated free products of weakly rigid factors and calculation of their symmetry groups (2005, methodology): “n applied to the case B = C our results become von Neumann algebra analogue of Kurosh’s classical theorems for free products of groups, similar in spirit to N. Ozawa’s recent results of this type in ([O2]), but covering a different class of factors than in ([O2]) and allowing amplifications. For insta”
- Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups (2006, background): “rs, it follows from [32] that L(Γ) does not embed in L∞(X,µ) ⋊G0 = (L∞(X,µ)⋊K0)⋊L0, the latter being the crossed product of an injective finite von Neumann algebra with a group in the class C of Ozawa [32]. Also, suppose that Λ is a property (T) group that contains two infinite commuting subgroups, on”
- Type III factors with unique Cartan decomposition (2012, background): “ II1 factors are obviously prime. We also mention here that a group belongs to class S if and only if it is exact and belongs to the above class QHreg of [CS11] (see e.g. [PV12, Proposition 2.7]). In [Oz04], it was proven that an arbitrary crossed product M= L∞(X)⋊Γ of a group Γ in class S and a pro”
- ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, background): “We did so by finding a “cohomological” characterization of Ozawa’s notion of bi-exactness [22].”
- Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups (2012, background): “ be in the class QH reg if Γ admits an array into an orthogonal representation that is weakly contained in the regular representation. The class QH reg is closely related to the class S introduced in [Oz04]. Recall from [Oz04, Section 4] that a countable group Γ is said to belong to this class if th”