A groupoid approach to L\"uck's amenability conjecture
Group Theory
2013-05-16 v2 K-Theory and Homology
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 L\"uck 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.
Cite
@article{arxiv.1205.1930,
title = {A groupoid approach to L\"uck's amenability conjecture},
author = {David Kyed and Henrik Densing Petersen},
journal= {arXiv preprint arXiv:1205.1930},
year = {2013}
}
Comments
30 pages; to appear in Osaka Journal of Mathematics