Abstract
We prove that amenability of a discrete group is equivalent to dimension flatness of certain ring inclusions naturally associated with measure preserving actions of the group. This provides a group-measure space theoretic solution to a conjecture of Lück stating that amenability of a group is characterized by dimension flatness of the inclusion of its complex group algebra into the associated von Neumann algebra.
Citation
David Kyed. Henrik D. Petersen. "A groupoid approach to Lück's amenability conjecture." Osaka J. Math. 51 (4) 905 - 935, October 2014.
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