English

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}.

Keywords

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

R2 v1 2026-07-22T17:08:51.665Z