An Introduction to Lie Groups and Lie Algebras

This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Alexander Kirillov, Jr (Author)

9780521889698, Cambridge University Press

Hardback, published 31 July 2008

236 pages
23.4 x 15.5 x 1.6 cm, 0.45 kg

'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

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.

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.

Subject Areas: Algebra [PBF]