Contractible Lie groups over local fields
Group Theory
2007-05-23 v1 Dynamical Systems
Abstract
Let G be a Lie group over a local field of positive characteristic which admits a contractive automorphism f (i.e., the forward iterates f^n(x) of each group element x converge to the neutral element 1). We show that then G is a torsion group of finite exponent and nilpotent. We also obtain results concerning the interplay between contractive automorphisms of Lie groups over local fields, contractive automorphisms of their Lie algebras, and positive gradations thereon. Some of the results even extend to Lie groups over arbitrary complete ultrametric fields.
Keywords
Cite
@article{arxiv.0704.3737,
title = {Contractible Lie groups over local fields},
author = {Helge Glockner},
journal= {arXiv preprint arXiv:0704.3737},
year = {2007}
}