Introduction to Lie Algebras

Lie theory is essential to many parts of mathematics and theoretical physics, and lie algebras have become a central subject in their own right. This is the first and only book to provide a basic algebraic introduction that has been designed specifically for undergraduates, and that covers all the core material required for all other work in Lie theory. Everything is kept as simple as possible so the only mathematics required is linear algebra, and there are plenty of worked examples and exercises making it ideal for self-study. This will be an essential text for lecturers and undergraduates in mathematics and theoretical physics.

The first and only basic introduction to Lie Algebras that's designed specifically for undergraduates Includes plenty of examples, exercises with solutions and problems, making it ideal for independent study Concludes with an overview of related topics and recent developments providing ideas for projects for further study Includes supplementary material: sn.pub/extras

Inhalt
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.