A groupoid approach to Lück's amenability conjecture

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.

30 pages; to appear in Osaka Journal of Mathematics

References in corpus (4)

• A spectral sequence to compute L2-Betti numbers of groups and groupoids
• L^2-Betti Numbers of Locally Compact Groups
• Amenability and vanishing of L^2-Betti numbers: an operator algebraic approach
• On the definition of L2-Betti numbers of equivalence relations