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| Author | : Roger William Carter |
| Publisher | : Cambridge University Press |
| Total Pages | : 662 |
| Release | : 2005-10-27 |
| Genre | : Mathematics |
| ISBN | : 9780521851381 |
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
| Author | : Roger William Carter |
| Publisher | : |
| Total Pages | : 632 |
| Release | : 2005 |
| Genre | : Lie algebras |
| ISBN | : 9780511200533 |
Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. A detailed Appendix is included.
| Author | : |
| Publisher | : |
| Total Pages | : 632 |
| Release | : 2005 |
| Genre | : Lie algebras |
| ISBN | : 9781139446723 |
| Author | : Neelacanta Sthanumoorthy |
| Publisher | : Academic Press |
| Total Pages | : 514 |
| Release | : 2016-04-26 |
| Genre | : Mathematics |
| ISBN | : 012804683X |
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 | : Cambridge University Press |
| Total Pages | : 428 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : 9780521466936 |
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.
| Author | : Minoru Wakimoto |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 332 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9780821826546 |
This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ...... root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.
| Author | : Victor G. Kac |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 267 |
| Release | : 2013-11-09 |
| Genre | : Mathematics |
| ISBN | : 1475713827 |
| Author | : Gerard G. A. Bäuerle |
| Publisher | : North Holland |
| Total Pages | : 420 |
| Release | : 1990 |
| Genre | : Finite element method |
| ISBN | : |
This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.
| Author | : Georgia Benkart |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 352 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : 0821851195 |
Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
| Author | : Alexander Vitalievich Razumov |
| Publisher | : Cambridge University Press |
| Total Pages | : 271 |
| Release | : 1997-05-15 |
| Genre | : Mathematics |
| ISBN | : 0521479231 |
The book describes integrable Toda type systems and their Lie algebra and differential geometry background.
