Contractible Lie groups over local fields

Details Contractible Lie groups over local fields Contractible Lie groups over local fields

2007-04-27

arxiv.org/abs/0704.3737v1

Mathematics

Group Theory

24 pages, LaTeX

Scientific paper

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.

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