Lectures On Lie Groups And Lie Algebras
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Lectures On Lie Groups And Lie Algebras
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Author : Roger W. Carter
language : en
Publisher: Cambridge University Press
Release Date : 1995-08-17
Lectures On Lie Groups And Lie Algebras written by Roger W. Carter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-17 with Mathematics categories.
Three of the leading figures in the field have composed this excellent introduction to the theory of Lie groups and Lie algebras. Together these lectures provide an elementary account of the theory that is unsurpassed. In the first part, Roger Carter concentrates on Lie algebras and root systems. In the second Graeme Segal discusses Lie groups. And in the final part, Ian Macdonald gives an introduction to special linear groups. Graduate students requiring an introduction to the theory of Lie groups and their applications should look no further than this book.
Lectures On Lie Groups
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Author : J. F. Adams
language : en
Publisher: University of Chicago Press
Release Date : 1982
Lectures On Lie Groups written by J. F. Adams and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
"[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
Lectures On Lie Groups And Lie Algebras
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Author : George D. Mostow
language : en
Publisher:
Release Date : 1963
Lectures On Lie Groups And Lie Algebras written by George D. Mostow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Group theory categories.
Lectures On Lie Groups And Lie Algebras
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Author : Roger William Carter
language : en
Publisher:
Release Date : 2014-05-14
Lectures On Lie Groups And Lie Algebras written by Roger William Carter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
An excellent introduction to the theory of Lie groups and Lie algebras.
Lectures On Lie Groups Second Edition
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Author : Hsiang Wu-yi
language : en
Publisher: World Scientific
Release Date : 2017-04-07
Lectures On Lie Groups Second Edition written by Hsiang Wu-yi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-07 with Mathematics categories.
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.
Lie Algebras And Lie Groups
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Author : Jean-Pierre Serre
language : en
Publisher: Springer
Release Date : 2009-02-07
Lie Algebras And Lie Groups written by Jean-Pierre Serre and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-07 with Mathematics categories.
The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x).
Lectures On Lie Groups And Lie Algebras
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Author : Roger William Carter
language : en
Publisher:
Release Date : 1995-08-17
Lectures On Lie Groups And Lie Algebras written by Roger William Carter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-17 with Mathematics categories.
An excellent introduction to the theory of Lie groups and Lie algebras.
Lectures On Exceptional Lie Groups
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Author : J. F. Adams
language : en
Publisher: University of Chicago Press
Release Date : 1996-12
Lectures On Exceptional Lie Groups written by J. F. Adams and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12 with Mathematics categories.
J. Frank Adams was internationally known and respected as one of the great algebraic topologists. Adams had long been fascinated with exceptional Lie groups, about which he published several papers, and he gave a series of lectures on the topic. The author's detailed lecture notes have enabled volume editors Zafer Mahmud and Mamoru Mimura to preserve the substance and character of Adams's work. Because Lie groups form a staple of most mathematics graduate students' diets, this work on exceptional Lie groups should appeal to many of them, as well as to researchers of algebraic geometry and topology. J. Frank Adams was Lowndean professor of astronomy and geometry at the University of Cambridge. The University of Chicago Press published his Lectures on Lie Groups and has reprinted his Stable Homotopy and Generalized Homology. Chicago Lectures in Mathematics Series
Lectures On Lie Groups
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Author : Wu Yi Hsiang
language : en
Publisher: World Scientific
Release Date : 2000
Lectures On Lie Groups written by Wu Yi Hsiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Lectures On Lie Groups And Lie Algebras Icm Edition
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Author : Carter
language : en
Publisher:
Release Date : 2014-12-01
Lectures On Lie Groups And Lie Algebras Icm Edition written by Carter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-01 with categories.