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Lie Algebras of Finite and Affine Type

Lie Algebras of Finite and Affine Type

£83.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: October 2005
  • availability: Available
  • format: Hardback
  • isbn: 9780521851381

£ 83.99
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  • 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 first half of the book deals with classification of the finite dimensional simple Lie algebras and of their finite dimensional irreducible representations. The second half introduces the theory of Kac-Moody algebras, concentrating particularly on those of affine type. A brief account of Borcherds algebras is also included. An Appendix gives a summary of the basic properties of each Lie algebra of finite and affine type.

    • This book, unlike similar titles, includes an account of both the theory of finite dimensional simple Lie Algebras and the more modern theory of Kac-Moody algebras
    • The mathematical treatment of the subject is thorough. Proofs are given in detail and the relaxed style makes this a user-friendly title
    • Roger Carter is a well known and respected author following the success of his earlier books on group theory and lie theory
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    Product details

    • Date Published: October 2005
    • format: Hardback
    • isbn: 9780521851381
    • length: 652 pages
    • dimensions: 236 x 159 x 35 mm
    • weight: 1.04kg
    • contains: 10 b/w illus.
    • availability: Available
  • Table of Contents

    1. Basic concepts
    2. Representations of soluble and nilpotent Lie algebras
    3. Cartan subalgebras
    4. The Cartan decomposition
    5. The root systems and the Weyl group
    6. The Cartan matrix and the Dynkin diagram
    7. The existence and uniqueness theorems
    8. The simple Lie algebras
    9. Some universal constructions
    10. Irreducible modules for semisimple Lie algebras
    11. Further properties of the universal enveloping algebra
    12. Character and dimension formulae
    13. Fundamental modules for simple Lie algebras
    14. Generalized Cartan matrices and Kac-Moody algebras
    15. The classification of generalised Cartan matrices
    16 The invariant form, root system and Weyl group
    17. Kac-Moody algebras of affine type
    18. Realisations of affine Kac-Moody algebras
    19. Some representations of symmetrisable Kac-Moody algebras
    20. Representations of affine Kac-Moody algebras
    21. Borcherds Lie algebras
    Appendix.

  • Author

    Roger Carter, University of Warwick
    Roger Carter is an Emeritus Professor of Mathematics at the University of Warwick.

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