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Every smooth p -adic Lie group admits a compatible analytic structure

Every smooth p -adic Lie group admits a compatible analytic structure We show that every finite-dimensional p -adic Lie group of class C k (where k ∈ ℕ ∪ {∞}) admits a C k -compatible analytic Lie group structure. We also construct an exponential map for every k + 1 times strictly differentiable ( SC k +1 ) ultrametric p -adic Banach-Lie group, which is an SC 1 -diffeomorphism and admits Taylor expansions of all finite orders ≤ k . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Every smooth p -adic Lie group admits a compatible analytic structure

Forum Mathematicum , Volume 18 (1) – Jan 26, 2006

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Publisher
de Gruyter
Copyright
© Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORUM.2006.003
Publisher site
See Article on Publisher Site

Abstract

We show that every finite-dimensional p -adic Lie group of class C k (where k ∈ ℕ ∪ {∞}) admits a C k -compatible analytic Lie group structure. We also construct an exponential map for every k + 1 times strictly differentiable ( SC k +1 ) ultrametric p -adic Banach-Lie group, which is an SC 1 -diffeomorphism and admits Taylor expansions of all finite orders ≤ k .

Journal

Forum Mathematicumde Gruyter

Published: Jan 26, 2006

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