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Semisimplicity and global dimension of a finite von Neumann algebra

Lia Vaš (2007)

Mathematica Bohemica

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

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