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p-Adic Lie Groups
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p-Adic Lie Groups
von: Peter Schneider
Springer-Verlag, 2011
ISBN: 9783642211478
259 Seiten, Download: 2268 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Introduction 6  
  Contents 9  
  Part A p-Adic Analysis and Lie Groups 12  
     I Foundations 13  
        1 Ultrametric Spaces 13  
        2 Nonarchimedean Fields 18  
        3 Convergent Series 24  
        4 Differentiability 27  
        5 Power Series 35  
        6 Locally Analytic Functions 48  
     II Manifolds 54  
        7 Charts and Atlases 54  
        8 Manifolds 56  
        9 The Tangent Space 65  
        10 The Topological Vector Space Can (M, E), Part 1 83  
        11 Locally Convex K-Vector Spaces 88  
        12 The Topological Vector Space Can (M, E), Part 2 93  
     III Lie Groups 98  
        13 Definitions and Foundations 98  
        14 The Universal Enveloping Algebra 110  
        15 The Concept of Free Algebras 115  
        16 The Campbell-Hausdorff Formula 120  
        17 The Convergence of the Hausdorff Series 133  
        18 Formal Group Laws 141  
  Part B The Algebraic Theory of p-Adic Lie Groups 163  
     IV Preliminaries 164  
        19 Completed Group Rings 164  
        20 The Example of the Group Zpd 170  
        21 Continuous Distributions 171  
        22 Appendix: Pseudocompact Rings 172  
     V p-Valued Pro-p-Groups 175  
        23 p-Valuations 175  
        24 The Free Group on Two Generators 181  
        25 The Operator P 184  
        26 Finite Rank Pro-p-Groups 187  
        27 Compact p-Adic Lie Groups 198  
     VI Completed Group Rings of p-Valued Groups 201  
        28 The Ring Filtration 201  
        29 Analyticity 207  
        30 Saturation 214  
     VII The Lie Algebra 224  
        31 A Normed Lie Algebra 224  
        32 The Hausdorff Series 237  
        33 Rational p-Valuations and Applications 248  
        34 Coordinates of the First and of the Second Kind 252  
  References 256  
  Index 258  


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