p-Adic Lie Groups

p-Adic Lie Groups by Peter Schneider.

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...

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Bibliographic Details
Main Author: Schneider, Peter (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Edition:1st ed. 2011.
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 344
Springer eBook Collection.
Subjects:
Topological groups.
Lie groups.
Associative rings.
Rings (Algebra).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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 Ĉan(M,E), part 1
  • II.11 Locally Convex K-Vector Spaces
  • II.12 The Topological Vector Space Ĉan(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 Ẑd_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.

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