Structural Results for Free Araki-woods Factors and Their Continuous Cores
نویسنده
چکیده
We show that for any type III1 free Araki-Woods factor M = Γ(HR, Ut) ′′ associated with an orthogonal representation (Ut) of R on a separable real Hilbert space HR, the continuous core M = M⋊σ R is a semisolid II∞ factor, i.e. for any non-zero finite projection q ∈ M , the II1 factor qMq is semisolid. If the representation (Ut) is moreover assumed to be mixing, then we prove that the core M is solid. As an application, we construct an example of a non-amenable solid II1 factor N with full fundamental group, i.e. F(N) = R∗+, which is not isomorphic to any interpolated free group factor L(Ft), for 1 < t ≤ +∞.
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