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Introduction to Lie Algebras

Paperback Engels 2011 1e druk 9781846280405
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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.

This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions.

Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Specificaties

ISBN13:9781846280405
Taal:Engels
Bindwijze:paperback
Aantal pagina's:251
Uitgever:Springer London
Druk:1

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Inhoudsopgave

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.

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€ 42,99
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        Introduction to Lie Algebras