Israel Journal of Mathematics

, Volume 173, Issue 1, pp 61–90 | Cite as

Rigid actions of amenable groups

  • Iddo SametEmail author


Given a countable discrete amenable group G, does there exist a free action of G on a Lebesgue probability space which is both rigid and weakly mixing? The answer to this question is positive if G is abelian. An affirmative answer is given in this paper, in the case that G is solvable or residually finite. For a locally finite group, the question is reduced to an algebraic one. It is exemplified how the algebraic question can be positively resolved for some groups, whereas for others the algebraic viewpoint suggests the answer may be negative.


Normal Subgroup Measure Preserve Cayley Graph Free Action Amenable Group 
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Copyright information

© Hebrew University Magnes Press 2009

Authors and Affiliations

  1. 1.Institute of MathematicsHebrew UniversityJerusalemIsrael

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