Lectures on Lie Groups and Representations of Locally Compact Groups
Author : François Bruhat
Publisher :
Page : 302 pages
File Size : 11,62 MB
Release : 1968
Category : Lie groups
ISBN :
Author : François Bruhat
Publisher :
Page : 302 pages
File Size : 11,62 MB
Release : 1968
Category : Lie groups
ISBN :
Author : Nicolas Bourbaki
Publisher :
Page : 0 pages
File Size : 43,77 MB
Release : 1968
Category :
ISBN :
Author :
Publisher :
Page : 135 pages
File Size : 13,8 MB
Release : 1958
Category :
ISBN :
Author : Alain Robert
Publisher : Cambridge University Press
Page : 217 pages
File Size : 47,70 MB
Release : 1983-02-10
Category : Mathematics
ISBN : 0521289750
Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.
Author : François Bruhat
Publisher :
Page : 270 pages
File Size : 43,81 MB
Release : 1963
Category : Lie groups
ISBN :
Author : Irving Kaplansky
Publisher : University of Chicago Press
Page : 161 pages
File Size : 23,3 MB
Release : 1971
Category : Mathematics
ISBN : 0226424537
This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.
Author : F. Bruhat
Publisher :
Page : pages
File Size : 43,26 MB
Release : 1958
Category :
ISBN :
Author : J. F. Adams
Publisher : University of Chicago Press
Page : 192 pages
File Size : 13,22 MB
Release : 1982
Category : Mathematics
ISBN : 0226005305
"[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky
Author : Wu-yi Hsiang
Publisher : World Scientific
Page : 161 pages
File Size : 33,88 MB
Release : 2017-04-07
Category : Mathematics
ISBN : 981474073X
This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive 'tour of revisiting' the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semi-simple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartan's theory on Lie groups and symmetric spaces.With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books.We begin our revisiting with the compact theory which is much simpler than that of the general semi-simple Lie theory; mainly due to the well fittings between the Frobenius-Schur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 1-4). It is a wonderful reality of the Lie theory that the clear-cut orbital geometry of the adjoint action of compact Lie groups on themselves (i.e. the geometry of conjugacy classes) is not only the key to understand the compact theory, but it actually already constitutes the central core of the entire semi-simple theory, as well as that of the symmetric spaces (cf. Lectures 5-9). This is the main reason that makes the succeeding generalizations to the semi-simple Lie theory, and then further to the Cartan theory on Lie groups and symmetric spaces, conceptually quite natural, and technically rather straightforward.
Author : Wu-yi Hsiang
Publisher : World Scientific
Page : 115 pages
File Size : 33,36 MB
Release : 2000-03-21
Category : Mathematics
ISBN : 9814495964
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.