Parameter rigid actions of simply connected nilpotent Lie groups (Q2874007)

It is shown that a locally free \(C^\infty\)-action of a connected and simply connected nilpotent Lie group on a compact manifold is parameter rigid if every real-valued cocycle is cohomologous to a constant cocycle. The converse is true if the action has a dense orbit. Using this, the author constructs parameter-rigid actions of simply connected nilpotent Lie groups whose Lie algebras admit rational structures with graduations.