With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York, Stony Brook, the book includes numerous exercises and worked examples, and is ideal for graduate courses on Lie groups and Lie algebras.
- The exposition emphasizes the main concepts rather than technical details of the proofs, making it possible to cover a lot of material in relatively concise work
- Numerous exercises and worked examples, as well as a sample syllabus, make this an ideal text for a graduate course on Lie groups and Lie algebras
- Focusses on semisimple Lie algebras and their representations; contains material rarely included in standard textbooks such as BGG resolution
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Reviews & endorsements
'… 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
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Product details
- Date Published: April 2017
- format: Paperback
- isbn: 9781316614105
- length: 234 pages
- dimensions: 230 x 153 x 14 mm
- weight: 0.36kg
- availability: Available
Table of Contents
Preface
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.
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Author
Alexander Kirillov, Jr, State University of New York, Stony Brook
Alexander Kirillov, Jr, is an Associate Professor in the Mathematics Department, State University of New York, Stony Brook. His research interests are representation theory, Lie algebras, quantum groups, affine Lie algebras and conformal field theory.