Kyed, DavidPetersen, Henrik D.2015-02-202015-02-202015-02-202014https://infoscience.epfl.ch/handle/20.500.14299/111652WOS:000346123300003We 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 Luck 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.text::journal::journal article::research article