Smooth Lie groups over local fields of positive characteristic need not be analytic
Group Theory
2007-05-23 v1
Abstract
We describe finite-dimensional smooth Lie groups over local fields of positive characteristic which do not admit an analytic Lie group structure compatible with the given topological group structure, and C^n-Lie groups without a compatible C^{n+1}-Lie group structure, for each positive integer n. We also present examples of non-analytic, smooth automorphisms of Lie groups over such fields, as well as C^n-automorphisms which fail to be C^{n+1}.
Cite
@article{arxiv.math/0408239,
title = {Smooth Lie groups over local fields of positive characteristic need not be analytic},
author = {Helge Glockner},
journal= {arXiv preprint arXiv:math/0408239},
year = {2007}
}
Comments
19 pages, LaTeX