Description
Book SynopsisThis graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style, this is a contemporary introduction to the subject. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.
Trade Review'… the exposition is very clear and logical. It has the advantage of giving the basic facts about Lie algebra theory with enough arguments but skipping the tedious technical details of proofs. Another excellent feature of the book is that many of the basic notions, properties and results are illustrated by a great number of exercises and examples. In my opinion this book is a nice addition to the landmarks in the field … I strongly recommend it to anyone wishing to enter into the beautiful and exciting field of Lie algebras and their applications.' Journal of Geometry and Symmetry in Physics
'… very readable … I strongly recommend this book as a possible selection for graduate courses, as well as for independent study, or individual reading.' MAA Reviews
'There are many exercises … The last appendix contains a useful detailed sample syllabus for a one-semester graduate course (two lectures a week).' EMS Newsletter
'The book is a very concise and nice introduction to Lie groups and Lie algebras. It seems to be well suited for a course on the subject.' Mathematical Reviews
Table of ContentsPreface; 1. Introduction; 2. Lie groups: basic definitions; 3. Lie groups and Lie algebras; 4. Representations of Lie groups and Lie algebras; 5. Structure theory of Lie algebras; 6. Complex semisimple Lie algebras; 7. Root systems; 8. Representations of semisimple Lie Algebras; Overview of the literature; A. Root systems and simple Lie algebras; B. Sample syllabus; List of notation; Index; Bibliography.
