Introduction to Lie Algebras

Authors:

ISBN: 978-1-84628-040-5 (Print) 978-1-84628-490-8 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-x

  2. No Access

    Book Chapter

    Pages 1-9

    Introduction

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    Book Chapter

    Pages 11-17

    Ideals and Homomorphisms

  4. No Access

    Book Chapter

    Pages 19-26

    Low-Dimensional Lie Algebras

  5. No Access

    Book Chapter

    Pages 27-36

    Solvable Lie Algebras and a Rough Classification

  6. No Access

    Book Chapter

    Pages 37-44

    Subalgebras of gl(V)

  7. No Access

    Book Chapter

    Pages 45-52

    Engel’s Theorem and Lie’s Theorem

  8. No Access

    Book Chapter

    Pages 53-65

    Some Representation Theory

  9. No Access

    Book Chapter

    Pages 67-76

    Representations of sl(2, C)

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    Book Chapter

    Pages 77-90

    Cartan’s Criteria

  11. No Access

    Book Chapter

    Pages 91-107

    The Root Space Decomposition

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    Book Chapter

    Pages 109-124

    Root Systems

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    Book Chapter

    Pages 125-139

    The Classical Lie Algebras

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    Book Chapter

    Pages 141-152

    The Classification of Root Systems

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    Book Chapter

    Pages 153-161

    Simple Lie Algebras

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    Book Chapter

    Pages 163-188

    Further Directions

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    Book Chapter

    Pages 189-208

    Appendix A: Linear Algebra

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    Book Chapter

    Pages 209-214

    Appendix B: Weyl’s Theorem

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    Book Chapter

    Pages 215-221

    Appendix C: Cartan Subalgebras

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    Book Chapter

    Pages 223-229

    Appendix D: Weyl Groups

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    Book Chapter

    Pages 231-246

    Appendix E: Answers to Selected Exercises

  22. Back Matter

    Pages 247-251