arXiv math/07025292007-02math.RAmath.OA

Semisimplicity and global dimension of a finite von Neumann algebra

Lia Vas

发表信息：: Mathematica Bohemica, 132 (2007), no. 1, 13 - 26

英文摘要：

We prove that a finite von Neumann algebra ${\mathcal A}$ is semisimple if the algebra of affiliated operators ${\mathcal U}$ of ${\mathcal A}$ is semisimple. When ${\mathcal A}$ is not semisimple, we give the upper and lower bounds for the global dimensions of ${\mathcal A}$ and ${\mathcal U}.$ This last result requires the use of the Continuum Hypothesis.

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