Introduction To Kac Moody Algebra

Author : Zhe-xian Wan
Publisher : World Scientific
ISBN 13 : 9814513903
Total Pages : 172 pages
Book Rating : 4.06/5 ( download)

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Download or read book Introduction To Kac-moody Algebras written by Zhe-xian Wan and published by World Scientific. This book was released on 1991-03-29 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a rapidly growing subject of modern mathematics, the Kac-Moody algebra, which was introduced by V Kac and R Moody simultanously and independently in 1968.

Author : Zhexian Wan
Publisher : World Scientific
ISBN 13 : 9789810202248
Total Pages : 178 pages
Book Rating : 4.45/5 ( download)

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Download or read book Introduction to Kac-Moody Algebra written by Zhexian Wan and published by World Scientific. This book was released on 1991 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a rapidly growing subject of modern mathematics, the Kac-Moody algebra, which was introduced by V Kac and R Moody simultanously and independently in 1968.

Author : Wan Zhe-xian
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.23/5 ( download)

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Download or read book Introduction to Kac-Moody Algebras written by Wan Zhe-xian and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Shrawan Kumar
Publisher : Springer Science & Business Media
ISBN 13 : 1461201055
Total Pages : 613 pages
Book Rating : 4.52/5 ( download)

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Download or read book Kac-Moody Groups, their Flag Varieties and Representation Theory written by Shrawan Kumar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.

Author : Victor G. Kac
Publisher : Springer Science & Business Media
ISBN 13 : 1475713827
Total Pages : 267 pages
Book Rating : 4.24/5 ( download)

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Download or read book Infinite Dimensional Lie Algebras written by Victor G. Kac and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Timothée Marquis
Publisher :
ISBN 13 : 9783037196878
Total Pages : 331 pages
Book Rating : 4.74/5 ( download)

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Download or read book An Introduction to Kac–Moody Groups Over Fields written by Timothée Marquis and published by . This book was released on 2018 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest for Kac–Moody algebras and groups has grown exponentially in the past decades, both in the mathematical and physics communities, and with it also the need for an introductory textbook on the topic. The aims of this book are twofold: - to offer an accessible, reader-friendly and self-contained introduction to Kac–Moody algebras and groups; - to clean the foundations and to provide a unified treatment of the theory. The book starts with an outline of the classical Lie theory, used to set the scene. Part II provides a self-contained introduction to Kac–Moody algebras. The heart of the book is Part III, which develops an intuitive approach to the construction and fundamental properties of Kac–Moody groups. It is complemented by two appendices, respectively offering introductions to affine group schemes and to the theory of buildings. Many exercises are included, accompanying the readers throughout their journey. The book assumes only a minimal background in linear algebra and basic topology, and is addressed to anyone interested in learning about Kac–Moody algebras and/or groups, from graduate (master) students to specialists.

Author : Roger William Carter
Publisher : Cambridge University Press
ISBN 13 : 9780521851381
Total Pages : 662 pages
Book Rating : 4.86/5 ( download)

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Download or read book Lie Algebras of Finite and Affine Type written by Roger William Carter and published by Cambridge University Press. This book was released on 2005-10-27 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough but relaxed mathematical treatment of Lie algebras.

Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
ISBN 13 : 012804683X
Total Pages : 512 pages
Book Rating : 4.38/5 ( download)

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Download or read book Introduction to Finite and Infinite Dimensional Lie (Super)algebras written by Neelacanta Sthanumoorthy and published by Academic Press. This book was released on 2016-04-26 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J.E. Humphreys
Publisher : Springer Science & Business Media
ISBN 13 : 1461263980
Total Pages : 189 pages
Book Rating : 4.82/5 ( download)

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Download or read book Introduction to Lie Algebras and Representation Theory written by J.E. Humphreys and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Peter Goddard
Publisher : World Scientific
ISBN 13 : 9789971504205
Total Pages : 610 pages
Book Rating : 4.00/5 ( download)

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Download or read book Kac-Moody and Virasoro Algebras written by Peter Goddard and published by World Scientific. This book was released on 1988 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reviews the subject of Kac-Moody and Virasoro Algebras. It serves as a reference book for physicists with commentary notes and reprints.