Lectures On Lie Groups

by Wu-yi Hsiang

Overview

This invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action, is regarded as the geometric organization of the totality of non-commutativity of a given compact connected Lie group, while the maximal tori theorem of É. Cartan and the Weyl reduction of the adjoint action on G to the Weyl group action on a chosen maximal torus are presented as the key results that provide a clear-cut understanding of the orbital geometry.

Product Details

ISBN-13:	9789810235222
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	03/22/2000
Series:	Series On University Mathematics , #2
Pages:	114
Product dimensions:	6.30(w) x 8.70(h) x 0.50(d)

Table of Contents

  Linear Groups and Linear Representations         1  Lie Groups and Lie Algebras                      20   Orbital Geometry of the Adjoint Action           38   Coxeter Groups, Weyl Reduction and Weyl          58   Formulas   Structural Theory of Compact Lie Algebras        78   Classification Theory of Compact Lie Algebras    93   and Compact Connected Lie Groups