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| Format: | Preprint |
| Published: |
2006
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0606271 |
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Table of Contents:
- We prove that certain free products of factors of type ${\rm I}$ 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 $λ, μ\in ]0, 1[$, we show that $$(M_2(\C), ω_λ) \ast (M_2(\C), ω_μ)$$ 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.