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 171 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.
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.
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:
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 2002-09-10 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Most of these topics appear here for the first time in book form. Many of them are interesting even in the classical case of semi-simple algebraic groups. Some appendices recall useful results from other areas, so the work may be considered self-contained, although some familiarity with semi-simple Lie algebras or algebraic groups is helpful. It is clear that this book is a valuable reference for all those interested in flag varieties and representation theory in the semi-simple or Kac-Moody case." —MATHEMATICAL REVIEWS "A lot of different topics are treated in this monumental work. . . . many of the topics of the book will be useful for those only interested in the finite-dimensional case. The book is self contained, but is on the level of advanced graduate students. . . . For the motivated reader who is willing to spend considerable time on the material, the book can be a gold mine. " —ZENTRALBLATT MATH
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.
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:
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.
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 514 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
Download or read book Introduction to Kac Moody Algebras written by J. Thierry-Mieg and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Kac Moody Lie Algebras and Related Topics written by Neelacanta Sthanumoorthy and published by American Mathematical Soc.. This book was released on 2004 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the proceedings of the Ramanujan International Symposium on Kac-Moody Lie algebras and their applications. The symposium provided researchers in mathematics and physics with the opportunity to discuss new developments in this rapidly-growing area of research. The book contains several excellent articles with new and significant results. It is suitable for graduate students and researchers working in Kac-Moody Lie algebras, their applications, and related areas of research.
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.
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.
Download or read book New Trends in Algebras and Combinatorics written by K. P. Shum and published by . This book was released on 2020 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Infinite Dimensional Lie Algebras written by Victor G. Kac and published by Cambridge University Press. This book was released on 1990 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third, substantially revised edition of a monograph concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris.
Download or read book Some Generalized Kac Moody Algebras with Known Root Multiplicities written by Peter Niemann and published by American Mathematical Soc.. This book was released on 2002 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
Download or read book Affine Lie Algebras Weight Multiplicities and Branching Rules written by Sam Kass and published by Univ of California Press. This book was released on 1990-01-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference. This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference.
