Skip to content
Register Sign in Wishlist

An Introduction to Lie Groups and Lie Algebras

$41.99 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: April 2017
  • availability: Available
  • format: Paperback
  • isbn: 9781316614105

$ 41.99 (P)

Add to cart Add to wishlist

Other available formats:
Hardback, eBook

Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.

    • The exposition emphasizes the main concepts rather than technical details of the proofs, making it possible to cover a lot of material in relatively concise work
    • Numerous exercises and worked examples, as well as a sample syllabus, make this an ideal text for a graduate course on Lie groups and Lie algebras
    • Focusses on semisimple Lie algebras and their representations; contains material rarely included in standard textbooks such as BGG resolution
    Read more

    Reviews & endorsements

    "The book is a very concise and nice introduction to Lie groups and Lie algebras. It seems to be well suited for a course on the subject. The exercises and examples will be useful in that case."
    Erik Koelink, Mathematical Reviews

    "I strongly recommend this book as a possible selection for graduate course(s), as well as independent study, or individual reading."
    Mihaela Poplicher, MAA Reviews

    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

    • Date Published: April 2017
    • format: Paperback
    • isbn: 9781316614105
    • length: 234 pages
    • dimensions: 230 x 153 x 14 mm
    • weight: 0.36kg
    • availability: Available
  • Table of Contents

    1. Introduction
    2. Lie groups: basic definitions
    3. Lie groups and Lie algebras
    4. Representations of Lie groups and Lie algebras
    5. Structure theory of Lie algebras
    6. Complex semisimple Lie algebras
    7. Root systems
    8. Representations of semisimple Lie Algebras
    Overview of the literature
    A. Root systems and simple Lie algebras
    B. Sample syllabus
    List of notation

  • Resources for

    An Introduction to Lie Groups and Lie Algebras

    Alexander Kirillov, Jr

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to instructors whose faculty status has been verified. To gain access to locked resources, instructors should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other instructors may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Instructors are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact

  • Author

    Alexander Kirillov, Jr, State University of New York, Stony Brook
    Alexander Kirillov, Jr, is an Associate Professor in the Mathematics Department, State University of New York, Stony Brook. His research interests are representation theory, Lie algebras, quantum groups, affine Lie algebras and conformal field theory.

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.