Geodesic
Semisimplicity and global dimension of a finite von Neumann algebra
Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 13-26

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MR Zbl
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.
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.
DOI : 10.21136/MB.2007.133990
Classification : 16E10, 16K99, 16W99, 46L10, 46L99
Keywords: finite von Neumann algebra; algebra of affiliated operators; semisimple ring; global dimension 
Vaš, Lia. Semisimplicity and global dimension of a finite von Neumann algebra. Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 13-26. doi: 10.21136/MB.2007.133990
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