Graduate Texts in Mathematics

Introduction to Lie Algebras and Representation Theory

Authors: HUMPHREYS, JAMES

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About this Textbook

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.

Table of contents (7 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-1-4612-6398-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.95
price for USA
  • ISBN 978-0-387-90053-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $69.95
price for USA
  • ISBN 978-0-387-90052-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Lie Algebras and Representation Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
9
Copyright
1972
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4612-6398-2
DOI
10.1007/978-1-4612-6398-2
Hardcover ISBN
978-0-387-90053-7
Softcover ISBN
978-0-387-90052-0
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIII, 173
Topics