Lie Algebras of Finite and Affine Type PDF Download
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Author: Roger William Carter
Publisher: Cambridge University Press
ISBN: 9780521851381
Category : Mathematics
Languages : en
Pages : 662
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Book Description
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author: Roger William Carter
Publisher: Cambridge University Press
ISBN: 9780521851381
Category : Mathematics
Languages : en
Pages : 662
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Book Description
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Author: Neelacanta Sthanumoorthy
Publisher: Academic Press
ISBN: 012804683X
Category : Mathematics
Languages : en
Pages : 514
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Book Description
Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. - Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory - Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities - Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras - Focuses on Kac-Moody algebras
Author: Victor G. Kac
Publisher: Springer Science & Business Media
ISBN: 1475713827
Category : Mathematics
Languages : en
Pages : 267
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Book Description
Author: Alexander Vitalievich Razumov
Publisher: Cambridge University Press
ISBN: 0521479231
Category : Mathematics
Languages : en
Pages : 271
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Book Description
The book describes integrable Toda type systems and their Lie algebra and differential geometry background.
Author: J.E. Humphreys
Publisher: Springer Science & Business Media
ISBN: 1461263980
Category : Mathematics
Languages : en
Pages : 189
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Book Description
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
Author: Alexander Molev
Publisher: American Mathematical Soc.
ISBN: 0821843745
Category : Mathematics
Languages : en
Pages : 422
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Book Description
The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.
Author: K. Erdmann
Publisher: Springer Science & Business Media
ISBN: 1846284902
Category : Mathematics
Languages : en
Pages : 254
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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.
Author: Jürgen Fuchs
Publisher: Cambridge University Press
ISBN: 9780521541190
Category : Mathematics
Languages : en
Pages : 464
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Book Description
This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.
Author: Peter Schneider
Publisher: Springer Science & Business Media
ISBN: 364221147X
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Manifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.
Author: Victor Kac
Publisher: Springer Science & Business Media
ISBN: 9780387962160
Category : Mathematics
Languages : en
Pages : 406
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Book Description
This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.
