An Introduction to Lie Groups and Lie Algebras [Hardcover]

This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.This 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.This 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.This classic 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. Lie theory, in its own right, has become regarded as a classical branch of mathematics. 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 at 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. The book is a very concise and nice introduction tl/