Skip to content
Infinite-Dimensional Lie Algebras

Infinite-Dimensional Lie Algebras

3rd Edition

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


Add to wishlist

Other available formats:

Looking for an inspection copy?

Please email to enquire about an inspection copy of this book

Product filter button
About the Authors
  • 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
    Read more

    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

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    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

    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
    Conference proceedings and collections of paper.

  • Author

    Victor G. Kac, Massachusetts Institute of Technology

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.