Structure and Geometry of Lie Groups

This text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students. Building on the authors' Lie-Gruppen und Lie-Algebren textbook from 1991, it presents the fundamental  principles of Li...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Hilgert, Joachim (Autor), Neeb, Karl-Hermann (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2012.
Edición:1st ed. 2012.
Colección:Springer Monographs in Mathematics,
Temas:
Topological groups.
Lie groups.
Geometry, Differential.
Algebraic topology.
Algebra.
Topological Groups and Lie Groups.
Differential Geometry.
Algebraic Topology.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • Preface
  • 1 Introduction
  • Part I Matrix Groups
  • 2 Concrete Matrix Groups
  • 3 The Matrix Exponential Function
  • 4 Linear Lie Groups
  • Part II Lie Algebras.- 5 Elementary Structure Theory of Lie Algebras.- 6 Root Decomposition.- 7 Representation Theory of Lie Algebras
  • Part III Manifolds and Lie Groups.- 8 Smooth Manifolds
  • 9 Basic Lie Theory
  • 10 Smooth Actions of Lie Groups
  • Part IV Structure Theory of Lie Groups
  • 11 Normal Subgroups, Nilpotemt and Solvable Lie Groups
  • 12 Compact Lie Groups
  • 13 Semisimple Lie Groups
  • 14 General Structure Theory
  • 15 Complex Lie Groups
  • 16 Linearity of Lie Groups
  • 17 Classical Lie Groups
  • 18 Nonconnected Lie Groups
  • Part V Appendices
  • A Basic Covering Theory
  • B Some Multilinear Algebra
  • C Some Functional Analysis
  • D Hints to Exercises
  • References
  • Index.

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