Representing interpolated free group factors as group factors
نویسندگان
چکیده
منابع مشابه
Interpolated Free Group Factors
The interpolated free group factors L(Fr) for 1 < r ≤ ∞, (also defined by F. Rădulescu) are given another (but equivalent) definition as well as proofs of their properties with respect to compression by projections and free products. In order to prove the addition formula for free products, algebraic techniques are developed which allow us to show R∗R ∼= L(F2) where R is the hyperfinite II1–fac...
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We give examples of non-amenable ICC groups Γ with the Haagerup property, weakly amenable with constant Λcb(Γ) = 1, for which we show that the associated II1 factors L(Γ) are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra P ⊂ L(Γ) generates an amenable von Neumann algebra. Nevertheless, for these examples of groups Γ, L(Γ) is not isomorphic to any interpolated free group...
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We show the existence of noncommutative random variables with finite free entropy but which do not generate a free group factor. In particular, this gives an example of variables X1, . . . , Xn such that δ(X1, . . . , Xn) = n while W ∗(X1, . . . , Xn) ≇ L(Fn).
متن کاملPopa Algebras in Free Group Factors
For each 1 < s < ∞, a Popa algebra As is constructed that embeds as a weakly dense C∗–subalgebra of the interpolated free group factor L(Fs). Certain approximation properties for As are shown. It follows that L(Fs) has the weak expectation property of Lance with respect to As. In the course of the demonstration, it is proved that under certain conditions, full amalgamated free products of matri...
متن کاملOn Ozawa’s Property for Free Group Factors
We give a new proof of a result of Ozawa showing that if a von Neumann subalgebra Q of a free group factor LFn, 2 ≤ n ≤ ∞ has relative commutant diffuse (i.e. without atoms), then Q is amenable.
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2020
ISSN: 1661-7207
DOI: 10.4171/ggd/565