Structure and Geometry of Lie Groups

Authors:

ISBN: 978-0-387-84793-1 (Print) 978-0-387-84794-8 (Online)

Table of contents (18 chapters)

  1. Front Matter

    Pages I-X

  2. No Access

    Book Chapter

    Pages 1-6

    Introduction

  3. Matrix Groups

    1. Front Matter

      Pages 7-7

    2. No Access

      Book Chapter

      Pages 9-37

      Concrete Matrix Groups

    3. No Access

      Book Chapter

      Pages 39-60

      The Matrix Exponential Function

    4. No Access

      Book Chapter

      Pages 61-76

      Linear Lie Groups

  4. Lie Algebras

    1. Front Matter

      Pages 77-77

    2. No Access

      Book Chapter

      Pages 79-132

      Elementary Structure Theory of Lie Algebras

    3. No Access

      Book Chapter

      Pages 133-166

      Root Decomposition

    4. No Access

      Book Chapter

      Pages 167-226

      Representation Theory of Lie Algebras

  5. Manifolds and Lie Groups

    1. Front Matter

      Pages 227-227

    2. No Access

      Book Chapter

      Pages 229-284

      Smooth Manifolds

    3. No Access

      Book Chapter

      Pages 285-358

      Basic Lie Theory

    4. No Access

      Book Chapter

      Pages 359-426

      Smooth Actions of Lie Groups

  6. Structure Theory of Lie Groups

    1. Front Matter

      Pages 427-427

    2. No Access

      Book Chapter

      Pages 429-458

      Normal Subgroups, Nilpotent and Solvable Lie Groups

    3. No Access

      Book Chapter

      Pages 459-503

      Compact Lie Groups

    4. No Access

      Book Chapter

      Pages 505-527

      Semisimple Lie Groups

    5. No Access

      Book Chapter

      Pages 529-563

      General Structure Theory

    6. No Access

      Book Chapter

      Pages 565-586

      Complex Lie Groups

    7. No Access

      Book Chapter

      Pages 587-604

      Linearity of Lie Groups

    8. No Access

      Book Chapter

      Pages 605-628

      Classical Lie Groups

    9. No Access

      Book Chapter

      Pages 629-649

      Nonconnected Lie Groups

  7. Back Matter

    Pages 651-744