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  • © 1972

Introduction to Lie Algebras and Representation Theory

Part of the book series: Graduate Texts in Mathematics (GTM, volume 9)

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  • ISBN: 978-1-4612-6398-2
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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
  2. Basic Concepts

    • James E. Humphreys
    Pages 1-14
  3. Semisimple Lie Algebras

    • James E. Humphreys
    Pages 15-41
  4. Root Systems

    • James E. Humphreys
    Pages 42-72
  5. Isomorphism and Conjugacy Theorems

    • James E. Humphreys
    Pages 73-88
  6. Existence Theorem

    • James E. Humphreys
    Pages 89-106
  7. Representation Theory

    • James E. Humphreys
    Pages 107-144
  8. Chevalley Algebras and Groups

    • James E. Humphreys
    Pages 145-164
  9. Back Matter

    Pages 165-177

About this book

This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incorĀ­ porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.

Keywords

  • Lie
  • algebra
  • algebraic geometry
  • automorphism
  • field
  • homomorphism
  • lie algebra
  • linear algebra
  • matrix
  • polynomial
  • representation theory
  • transformation

Authors and Affiliations

  • University of Massachusetts, Amherst, USA

    James E. Humphreys

Bibliographic Information

  • Book Title: Introduction to Lie Algebras and Representation Theory

  • Authors: James E. Humphreys

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-6398-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1972

  • Hardcover ISBN: 978-0-387-90053-7

  • Softcover ISBN: 978-0-387-90052-0

  • eBook ISBN: 978-1-4612-6398-2

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XIII, 173

  • Topics: Algebra

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-6398-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 69.95
Price excludes VAT (USA)
Hardcover Book USD 69.95
Price excludes VAT (USA)