On Some Free Products of Von Neumann Algebras which are Free Araki–Woods Factors
On Some Free Products of Von Neumann Algebras which are Free Araki–Woods Factors
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论冯·诺依曼代数的一些自由乘积即自由Araki-Woods因子
DOI：
10.1093/imrn/rnm098
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发表时间：
2006
影响因子：
1
通讯作者：
Cyril Houdayer
中科院分区：
文献类型：
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作者：
Cyril Houdayer
证明了I型因子和其它von Neumann代数关于非迹概周期态的自由积是概周期自由Araki-Woods因子。特别地，它们具有自由吸收性质，Connes的Sd不变量将这些自由产物完全分类。例如，对于λ，μ ∈]0，1[，我们证明了（M2（C），ωλ）*（M2（C），ωμ）同构于自由Araki-Woods因子，其Sd不变量是由λ和μ生成的R+* 的子群.我们的证明是基于代数技术和合并的自由产品。这些结果回答了Dykema和Shlyakhtenko的一些问题。
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.