Smooth Lie groups over local fields of positive characteristic need not be analytic

Details Smooth Lie groups over local fields of positive characteristic need not be analytic Smooth Lie groups over local fields of positive characteristic need not be analytic

2004-08-18

arxiv.org/abs/math/0408239v1

Mathematics

Group Theory

19 pages, LaTeX

Scientific paper

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}.

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