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p-Adic Lie Groups
Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the disc...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2011.
|
| Edición: | 1st ed. 2011. |
| Colección: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
344 |
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- Introduction
- Part A: p-Adic Analysis and Lie Groups
- I.Foundations
- I.1.Ultrametric Spaces
- I.2.Nonarchimedean Fields
- I.3.Convergent Series
- I.4.Differentiability
- I.5.Power Series
- I.6.Locally Analytic Functions.- II.Manifolds
- II.7.Charts and Atlases
- II.8.Manifolds
- II.9.The Tangent Space
- II.10.The Topological Vector Space C^an(M,E), part 1
- II.11 Locally Convex K-Vector Spaces
- II.12 The Topological Vector Space C^an(M,E), part 2
- III.Lie Groups
- III.13.Definitions and Foundations
- III.14.The Universal Enveloping Algebra
- III.15.The Concept of Free Algebras
- III.16.The Campbell-Hausdorff Formula
- III.17.The Convergence of the Hausdorff Series
- III.18.Formal Group Laws
- Part B:The Algebraic Theory of p-Adic Lie Groups
- IV.Preliminaries
- IV.19.Completed Group Rings
- IV.20.The Example of the Group Z^d_p
- IV.21.Continuous Distributions
- IV.22.Appendix: Pseudocompact Rings
- V.p-Valued Pro-p-Groups
- V.23.p-Valuations
- V.24.The free Group on two Generators
- V.25.The Operator P
- V.26.Finite Rank Pro-p-Groups
- V.27.Compact p-Adic Lie Groups
- VI.Completed Group Rings of p-Valued Groups
- VI.28.The Ring Filtration
- VI.29.Analyticity
- VI.30.Saturation
- VII.The Lie Algebra
- VII.31.A Normed Lie Algebra
- VII.32.The Hausdorff Series
- VII.33.Rational p-Valuations and Applications
- VII.34.Coordinates of the First and of the Second Kind
- References
- Index.