Inventiones mathematicae

, Volume 51, Issue 2, pp 171–188

Groups admitting ergodic actions with generalized discrete spectrum

  • Calvin C. Moore
  • Robert J. Zimmer
Article

Abstract

The class of groups admitting an effective ergodic action with generalized discrete spectrum is a natural generalization of the class of maximally almost periodic groups. H. Freudenthal has given a complete characterization of the connected maximally almost periodic groups, and here we give a complete characterization of the almost connected groups admitting an effective ergodic action with generalized discrete spectrum. Namely, we show that an almost connected group is in this class if and only if it is typeR. It is known that this is equivalent to the group being of polynomial growth, and for Lie groups is just the condition that all eigenvalues of the adjoint representation lie on the unit circle.

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Calvin C. Moore
    • 1
  • Robert J. Zimmer
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicago

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