Semisimplicity and global dimension of a finite von Neumann algebra

Details Semisimplicity and global dimension of a finite von Neumann algebra Semisimplicity and global dimension of a finite von Neumann algebra

2007-02-18

arxiv.org/abs/math/0702529v2

Mathematica Bohemica, 132 (2007), no. 1, 13 - 26

Mathematics

Rings and Algebras

Scientific paper

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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