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

JOURNAL OF ALGEBRA

卷:285

Article

Glöckner, H

关键词: smooth Lie group;    analytic Lie group;    totally disconnected group;    finite order differentiability;    local field;    positive characteristic;    contractive automorphism;    scale function;    tidy subgroup;    Willis theory;    non-archimedian analysis;   

DOI  :  10.1016/j.jalgebra.2004.11.018

来源: Elsevier

【 摘 要 】

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 Cn+1-Lie group structure for each n greater than or equal to. 1. We also present examples of non-analytic, smooth automorphisms of analytic Lie groups over such fields, as well as C-n-automorphisms which fail to be Cn+1. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free