Free products of hyperfinite von Neumann algebras and free dimension
Free products of hyperfinite von Neumann algebras and free dimension
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超有限冯诺依曼代数和自由维的自由积
DOI：
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发表时间：
1992
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通讯作者：
Ken Dykema
中科院分区：
文献类型：
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作者：
Ken Dykema
研究了任意一对有限超有限von Neumann代数的自由积，确定了它是一个有限维代数与一个插值自由群因子$L(FreFr)$的直和.有限维部分依赖于原始代数的最小投影，而自由群因子部分的“维”r是利用自由维的概念得到的。对于离散的顺从群G$和H$，这意味着群von Neumann代数$L(G*H)$是插值自由群因子，并且仅依赖于G$和H$的阶数.
The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated free group factor $L(freeF_r)$. The finite dimensional part depends on the minimal projections of the original algebras and the "dimension", r, of the free group factor part is found using the notion of free dimension. For discrete amenable groups $G$ and $H$ this implies that the group von Neumann algebra $L(G*H)$ is an interpolated free group factor and depends only on the orders of $G$ and $H$.