Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states
Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states
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有限维和其他冯诺依曼代数关于非迹态的自由积
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
K. Dykema
中科院分区：
文献类型：
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作者：
K. Dykema
本文证明了任意有限维von Neumann代数关于任意忠实态的von Neumann代数自由积是有限维代数的III型因子可能直和.Ⅲ型因子上的自由积态是我们称之为极值概周期态，并且有中心化子同构于$L（freeF_infty）$。这允许进一步分类的III型因子，并提供了另一个完整的III型因子具有任意$Sd$~康纳斯不变量的建设。本文所考虑的自由积并不局限于有限维代数的自由积，而是一种相当一般的形式。
The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type~III factor possibly direct sum a finite dimensional algebra. The free product state on the type~III factor is what we call an extremal almost periodic state, and has centralizer isomorphic to $L(freeF_infty)$. This allows further classification the type~III factor and provides another construction of full type~III$_1$ factors having arbitrary $Sd$~invariant of Connes. The free products considered in this paper are not limited to free products of finite dimensional algebras, but can be of a quite general form.