num_pages: 114
description: 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 . 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.
language: English
title: Lectures on Lie Groups
publisher: World Scientific Publishing Company