Structure and Geometry of Lie Groups

• Main Authors: Hilgert, Joachim (Author), Neeb, Karl-Hermann (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2012.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebra.; Topological groups.; Lie groups.; Differential geometry.; Algebraic topology.; Topological Groups, Lie Groups.; Differential Geometry.; Algebraic Topology.

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...

Table of Contents:

• 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.