Author: Roger William CarterPublisher:
ISBN: 9780521499224
Category : Mathematics
Languages : en
Pages : 190
Book Description
An excellent introduction to the theory of Lie groups and Lie algebras.
Lectures on Lie Groups and Lie Algebras
Author: Roger William CarterPublisher:
ISBN: 9780521499224
Category : Mathematics
Languages : en
Pages : 190
Book Description
An excellent introduction to the theory of Lie groups and Lie algebras.
Lectures on Lie Groups
Author: J. F. AdamsPublisher: University of Chicago Press
ISBN: 0226005305
Category : Mathematics
Languages : en
Pages : 192
Book Description
"[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
Lie Algebras and Lie Groups
Author: Jean-Pierre SerrePublisher: Springer
ISBN: 3540706348
Category : Mathematics
Languages : en
Pages : 180
Book Description
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).
An Introduction to Lie Groups and Lie Algebras
Author: Alexander A. KirillovPublisher: Cambridge University Press
ISBN: 0521889693
Category : Mathematics
Languages : en
Pages : 237
Book Description
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Lectures On Lie Groups (Second Edition)
Author: Wu-yi HsiangPublisher: World Scientific
ISBN: 981474073X
Category : Mathematics
Languages : en
Pages : 161
Book Description
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.
Lectures on Exceptional Lie Groups
Author: J. F. AdamsPublisher: University of Chicago Press
ISBN: 9780226005270
Category : Mathematics
Languages : en
Pages : 20
Book Description
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
Introduction to Lie Algebras
Author: K. ErdmannPublisher: Springer Science & Business Media
ISBN: 1846284902
Category : Mathematics
Languages : en
Pages : 254
Book Description
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.
Representation Theory
Author: William FultonPublisher: Springer Science & Business Media
ISBN: 9780387974958
Category : Mathematics
Languages : en
Pages : 616
Book Description
Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.
Lectures on Lie Groups
Author: Wu Yi HsiangPublisher: World Scientific
ISBN: 9789810235291
Category : Mathematics
Languages : en
Pages : 118
Book 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.
Applications of Lie Groups to Differential Equations
Author: Peter J. OlverPublisher: Springer Science & Business Media
ISBN: 1468402749
Category : Mathematics
Languages : en
Pages : 524
Book Description
This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.