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Semisimplicity and global dimension of a finite von Neumann algebra

Lia Vas
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Abstract

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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Lia Vas. 2007-10-30. Semisimplicity and global dimension of a finite von Neumann algebra. https://arxiv.org/abs/math/0702529

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