Lie Algebras of Finite and Affine Type

Name: Lie Algebras of Finite and Affine Type
Price: 105.02 USD
Availability: InStock
ISBN: 9780521851381

ISBN-10: 0521851386

ISBN-13: 9780521851381

Edition: 2005

Authors: Roger Carter, B. Bollobas, W. Fulton, A. Katok, F. Kirwan

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Description:

Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. The Appendix provides a summary of the basic properties of each Lie algebra of finite and affine type.

Book details

List price: $134.99
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 10/27/2005
Binding: Hardcover
Pages: 650
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 2.552
Language: English




Basic concepts



Representations of soluble and nilpotent Lie algebras



Cartan subalgebras



The Cartan decomposition



The root systems and the Weyl group



The Cartan matrix and the Dynkin diagram



The existence and uniqueness theorems



The simple Lie algebras



Some universal constructions



Irreducible modules for semisimple Lie algebras



Further properties of the universal enveloping algebra



Character and dimension formulae



Fundamental modules for simple Lie algebras



Generalized Cartan matrices and Kac-Moody algebras



The classification of generalised Cartan matrices



The invariant form, root system and Weyl group



Kac-Moody algebras of affine type



Realisations of affine Kac-Moody algebras



Some representations of symmetrisable Kac-Moody algebras



Representations of affine Kac-Moody algebras



Borcherds Lie algebras


Appendix