Abstract
LetG be a countable discrete group acting by measure-preserving automorphisms of a finite measure space (M, μ) and let\(\mathfrak{N}\)(G,M) be the corresponding group measure space von Neumann algebra, which will be a finite von Neumann algebra. Necessary and sufficient conditions are given for\(\mathfrak{N}\)(G,M) to have a non-zero type I part, and the projection on the type I part is explicitly described.
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This research was supported in part by National Science Foundation Grant MCS 74-19876.
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Rieffel, M.A. The type of group measure space von Neumann algebras. Monatshefte für Mathematik 85, 149–162 (1978). https://doi.org/10.1007/BF01297544
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DOI: https://doi.org/10.1007/BF01297544