MATHEMATICA BOHEMICA, Vol. 132, No. 1, pp. 13-26 (2007)

Semisimplicity and global dimension of a finite
von Neumann algebra

Lia Vas

Lia Vas, Department of Mathematics, Physics and Computer Science, University of the Sciences in Philadelphia, 600 S. 43rd St., Philadelphia, PA 19104, e-mail:

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.

Keywords: finite von Neumann algebra, algebra of affiliated operators, semisimple ring, global dimension

Classification (MSC2000): 16W99, 46L10, 46L99, 16K99

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