Every smooth p-adic Lie group admits a compatible analytic structure
Identifieur interne : 000B72 ( Main/Exploration ); précédent : 000B71; suivant : 000B73Every smooth p-adic Lie group admits a compatible analytic structure
Auteurs : Helge Glöckner [Allemagne]Source :
- Forum Mathematicum [ 0933-7741 ] ; 2006-01-26.
English descriptors
- KwdEn :
- Absolute value, Akxk, Analytic structure, Analytic structures, Banach, Continuous groups, Continuous homomorphism, Continuous mapping, Continuous maps, Continuous seminorm, Ekxk, Eld, Expg, Exponential, Glockner, Group structure, Homogeneous polynomial, Homomorphism, Identity neighbourhood, Inequality, Invariant vector, Inverse function theorem, Isometry, Kgsx, Lemma, Logg, Manifold structure, Maximum norm, Modelled, Neighbourhood, Nite, Nite extension, Nite orders, Normed, Normed space, Normed spaces, Normed vector space, Notational formalism, Open identity neighbourhood, Open subgroup, Open subset, Order taylor expansion, Other hand, Polynormed space, Resp, Second assertion, Subgroup, Subset, Surjective, Surjective isometry, Taylor expansion, Taylor expansions, Topological, Topological group, Topological vector spaces, Topology, Ultrametric, Ultrametric banach space, Ultrametric group, Ultrametric inequality, Vector space, Vector spaces.
- Teeft :
- Absolute value, Akxk, Analytic structure, Analytic structures, Banach, Continuous groups, Continuous homomorphism, Continuous mapping, Continuous maps, Continuous seminorm, Ekxk, Eld, Expg, Exponential, Glockner, Group structure, Homogeneous polynomial, Homomorphism, Identity neighbourhood, Inequality, Invariant vector, Inverse function theorem, Isometry, Kgsx, Lemma, Logg, Manifold structure, Maximum norm, Modelled, Neighbourhood, Nite, Nite extension, Nite orders, Normed, Normed space, Normed spaces, Normed vector space, Notational formalism, Open identity neighbourhood, Open subgroup, Open subset, Order taylor expansion, Other hand, Polynormed space, Resp, Second assertion, Subgroup, Subset, Surjective, Surjective isometry, Taylor expansion, Taylor expansions, Topological, Topological group, Topological vector spaces, Topology, Ultrametric, Ultrametric banach space, Ultrametric group, Ultrametric inequality, Vector space, Vector spaces.
Abstract
We show that every finite-dimensional p-adic Lie group of class Ck (where k ∈ ℕ ∪ {∞}) admits a Ck -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.
Url:
DOI: 10.1515/FORUM.2006.003
Affiliations:
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Le document en format XML
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<term>Lemma</term>
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<front><div type="abstract" xml:lang="en">We show that every finite-dimensional p-adic Lie group of class Ck (where k ∈ ℕ ∪ {∞}) admits a Ck -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.</div>
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