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Parameter rigid actions of simply connected nilpotent Lie groups

Published online by Cambridge University Press:  22 August 2012

HIROKAZU MARUHASHI
HIROKAZU MARUHASHI*
Affiliation:
Department of Mathematics, Kyoto University, Japan (email: h-maruha@math.kyoto-u.ac.jp)
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Abstract

We show that for a locally free $C^{\infty }$-action of a connected and simply connected nilpotent Lie group on a compact manifold, if every real-valued cocycle is cohomologous to a constant cocycle, then the action is parameter rigid. The converse is true if the action has a dense orbit. Using this, we construct parameter rigid actions of simply connected nilpotent Lie groups whose Lie algebras admit rational structures with graduations. This generalizes the results of dos Santos [Parameter rigid actions of the Heisenberg groups. Ergod. Th. & Dynam. Sys.27(2007), 1719–1735] concerning the Heisenberg groups.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 6 , December 2013 , pp. 1864 - 1875
Copyright
Copyright © 2012 Cambridge University Press 

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References

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