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arXiv · 1205.1930

A groupoid approach to Lück's amenability conjecture

David Kyed·Henrik Densing Petersen
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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.

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David Kyed, Henrik Densing Petersen. 2013-05-15. A groupoid approach to Lück's amenability conjecture. https://arxiv.org/abs/1205.1930

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