# MathSciDoc: An Archive for Mathematician ∫

#### Mathematical PhysicsRings and Algebrasmathscidoc:1701.22004

Arkiv for Matematik, 50, (1), 165-182, 2010.1
The action of a Lie pseudogroup $\mathcal{G}$ on a smooth manifold$M$induces a prolonged pseudogroup action on the jet spaces$J$^{$n$}of submanifolds of$M$. We prove in this paper that both the local and global freeness of the action of $\mathcal{G}$ on$J$^{$n$}persist under prolongation in the jet order$n$. Our results underlie the construction of complete moving frames and, indirectly, their applications in the identification and analysis of the various invariant objects for the prolonged pseudogroup actions.
@inproceedings{peter2010persistence,
title={Persistence of freeness for Lie pseudogroup actions},
author={Peter J. Olver, and Juha Pohjanpelto},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203631166161009},
booktitle={Arkiv for Matematik},
volume={50},
number={1},
pages={165-182},
year={2010},
}

Peter J. Olver, and Juha Pohjanpelto. Persistence of freeness for Lie pseudogroup actions. 2010. Vol. 50. In Arkiv for Matematik. pp.165-182. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203631166161009.