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＜電子ブック＞
p-Adic Lie Groups / by Peter Schneider
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 344)

版	1st ed. 2011.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2011
本文言語	英語
大きさ	XII, 256 p : online resource
著者標目	*Schneider, Peter author SpringerLink (Online service)
件　名	LCSH:Topological groups LCSH:Lie groups LCSH:Associative rings LCSH:Associative algebras FREE:Topological Groups and Lie Groups FREE:Associative Rings and Algebras
一般注記	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 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 discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings HTTP:URL=https://doi.org/10.1007/978-3-642-21147-8

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