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Infinite-Dimensional Lie Algebras

Infinite-Dimensional Lie Algebras

3rd Edition

  • Date Published: December 1994
  • availability: Available
  • format: Paperback
  • isbn: 9780521466936

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  • This is the third, substantially revised edition of this important monograph. The book is concerned with Kac–Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.

    • Highly acclaimed in its hardback edition
    • Of interest to mathematical physicists as well as algebraists
    • Kac is one of the best-known names in this field; he is one of the founders of the subject
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    Reviews & endorsements

    'A clear account of Kac–Moody algebras by one of the founders … Eminently suitable as an introduction … with a surprising number of exercises.' American Mathematical Monthly

    ' … a useful contribution. All the basic elements of the subject are covered … Many results which were previously scattered about in the literature are collected here … The book also contains many exercises and useful comments …' Physics in Canada

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    Product details

    • Edition: 3rd Edition
    • Date Published: December 1994
    • format: Paperback
    • isbn: 9780521466936
    • length: 424 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.62kg
    • availability: Available
  • Table of Contents

    Introduction
    Notational conventions
    1. Basic definitions
    2. The invariant bilinear form and the generalized casimir operator
    3. Integrable representations of Kac-Moody algebras and the weyl group
    4. A classification of generalized cartan matrices
    5. Real and imaginary roots
    6. Affine algebras: the normalized cartan invariant form, the root system, and the weyl group
    7. Affine algebras as central extensions of loop algebras
    8. Twisted affine algebras and finite order automorphisms
    9. Highest-weight modules over Kac-Moody algebras
    10. Integrable highest-weight modules: the character formula
    11. Integrable highest-weight modules: the weight system and the unitarizability
    12. Integrable highest-weight modules over affine algebras
    13. Affine algebras, theta functions, and modular forms
    14. The principal and homogeneous vertex operator constructions of the basic representation
    Index of notations and definitions
    References
    Conference proceedings and collections of paper.

  • Author

    Victor G. Kac, Massachusetts Institute of Technology

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