Introduction to Lie Algebras
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. Based on a lecture course given to fourth-year undergraduates, this book provides an elementary introduction to Lie algebras. It...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
London
Springer London
2006, 2006
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| Edition: | 1st ed. 2006 |
| Series: | Springer Undergraduate Mathematics Series
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Ideals and Homomorphisms
- Low-Dimensional Lie Algebras
- Solvable Lie Algebras and a Rough Classification
- Subalgebras of gl(V)
- Engel’s Theorem and Lie’s Theorem
- Some Representation Theory
- Representations of sl(2, C)
- Cartan’s Criteria
- The Root Space Decomposition
- Root Systems
- The Classical Lie Algebras
- The Classification of Root Systems
- Simple Lie Algebras
- Further Directions
- Appendix A: Linear Algebra
- Appendix B: Weyl’s Theorem
- Appendix C: Cartan Subalgebras
- Appendix D: Weyl Groups
- Appendix E: Answers to Selected Exercises