000			04002nam a22004935i 4500
001			978-3-642-21147-8
003			DE-He213
005			20140220083803.0
007			cr nn 008mamaa
008			110610s2011 gw | s |||| 0|eng d
020			_a9783642211478 _9978-3-642-21147-8
024	7		_a10.1007/978-3-642-21147-8 _2doi
050		4	_aQA252.3
050		4	_aQA387
072		7	_aPBG _2bicssc
072		7	_aMAT014000 _2bisacsh
072		7	_aMAT038000 _2bisacsh
082	0	4	_a512.55 _223
082	0	4	_a512.482 _223
100	1		_aSchneider, Peter. _eauthor.
245	1	0	_ap-Adic Lie Groups _h[electronic resource] / _cby Peter Schneider.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2011.
300			_aXII, 256 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, _x0072-7830 ; _v344
505	0		_aIntroduction -- 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.
520			_aManifolds 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.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aTopological Groups.
650	1	4	_aMathematics.
650	2	4	_aTopological Groups, Lie Groups.
650	2	4	_aAssociative Rings and Algebras.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642211461
830		0	_aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, _x0072-7830 ; _v344
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-21147-8
912			_aZDB-2-SMA
999			_c107911 _d107911