On Some Free Products of Von Neumann Algebras Which Are Free Araki-woods Factors
نویسنده
چکیده
We prove that certain free products of factors of type I and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption property and Connes’ Sd invariant completely classifies these free products. For example, for λ, μ ∈]0, 1[, we show that (M2(C), ωλ) ∗ (M2(C), ωμ) is isomorphic to the free Araki-Woods factor whose Sd invariant is the subgroup of R∗+ generated by λ and μ. Our proofs are based on algebraic techniques and amalgamated free products. These results give some answers to questions of Dykema and Shlyakhtenko.
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