P-Adic Lie Groups

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In addition to providing a self-contained introduction to p-adic lie groups, this volume discusses spaces of locally analytic functions as topological vector spaces, important to applications in representation theory.

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Title Statements

Full title :P-Adic Lie Groups.

Summary

Edition Statements

Publication Date:2011.

Publication Statements

Publisher(s):Springer Berlin Heidelberg
Place of Publication:Berlin, Heidelberg
Language:eng
Publication Date:2011.

The Physical Object

Description:1 online resource (258 pages).

Edition Identifiers

ISBN:3642211461, 9783642211461
DOI:10.1007/978-3-642-21147-8
oclc:ocn990537646
LC Classification:QA387
Dewey Decimal:512.55

Introduction; Contents; Part A p-Adic Analysis and Lie Groups; I Foundations; 1 Ultrametric Spaces; 2 Nonarchimedean Fields; 3 Convergent Series; 4 Differentiability; 5 Power Series; 6 Locally Analytic Functions; II Manifolds; 7 Charts and Atlases; 8 Manifolds; 9 The Tangent Space; 10 The Topological Vector Space Can (M, E), Part 1; 11 Locally Convex K-Vector Spaces; 12 The Topological Vector Space Can (M, E), Part 2; III Lie Groups; 13 Definitions and Foundations; 14 The Universal Enveloping Algebra; 15 The Concept of Free Algebras; 16 The Campbell-Hausdorff Formula.

17 The Convergence of the Hausdorff Series18 Formal Group Laws; Part B The Algebraic Theory of p-Adic Lie Groups; IV Preliminaries; 19 Completed Group Rings; 20 The Example of the Group Zpd; 21 Continuous Distributions; 22 Appendix: Pseudocompact Rings; V p-Valued Pro-p-Groups; 23 p-Valuations; 24 The Free Group on Two Generators; 25 The Operator P; 26 Finite Rank Pro-p-Groups; 27 Compact p-Adic Lie Groups; VI Completed Group Rings of p-Valued Groups; 28 The Ring Filtration; 29 Analyticity; 30 Saturation; VII The Lie Algebra; 31 A Normed Lie Algebra; 32 The Hausdorff Series.

33 Rational p-Valuations and Application…