Introduction to Lie Algebras

• Main Authors: Erdmann, Karin (Author), Wildon, Mark J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2006.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Algebra.; Physics.; Theoretical, Mathematical and Computational Physics.; Mathematical Methods in Physics.

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...

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.