Parameter rigid actions of simply connected nilpotent Lie groups
Group Theory
2021-03-24 v3 Dynamical Systems
Abstract
We show that for a locally free action of a 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.
Cite
@article{arxiv.1101.4161,
title = {Parameter rigid actions of simply connected nilpotent Lie groups},
author = {Hirokazu Maruhashi},
journal= {arXiv preprint arXiv:1101.4161},
year = {2021}
}
Comments
14 pages, no figures, typos corrected