Abstract
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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