We show that any free product of finite-dimensional von Neumann algebras equipped with non-tracial states is isomorphic to a free Araki–Woods factor with its free quasi-free state possibly direct sum a finite-dimensional von Neumann algebra. This gives a complete answer to questions posed by Dykema in [5] and Shlyakhtenko in [10], which had been partially answered by Houdayer in [7] and Ueda in [16]. We also extend this to suitable infinite-dimensional von Neumann algebras with almost periodic states.

中文翻译：

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用自由Araki–Woods因子表示的有限维和其他von Neumann代数的自由积

我们证明，配备有非种族态的有限维冯·诺伊曼代数的任何自由积都同自由Araki–Woods因子同构，其自由准自由态可能直接和有限维冯·诺伊曼代数的总和。这完全回答了由[5]中的Dykema和[10]中的Shlyakhtenko提出的问题，这些问题已由Houdayer [7]和Ueda在[16]中部分回答。我们还将其扩展到具有几乎周期状态的合适的无限维冯·诺伊曼代数。