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Graduate Texts in Mathematics

Lie Groups, Lie Algebras, and Representations

An Elementary Introduction

Authors: Hall, Brian C.

  • New edition extensively revised and updated
  • Covers the core topics of Lie theory from an elementary point of view
  • Includes many new exercises
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eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-13467-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-13466-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 4, 2016
  • ISBN 978-3-319-37433-8
  • Free shipping for individuals worldwide
About this Textbook

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.

In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:

  • a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras
  • motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C)
  • an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras
  • a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments

The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.

Review of the first edition:

This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.

— The Mathematical Gazette

About the authors

Brian Hall is Professor of Mathematics at the University of Notre Dame, IN.

Reviews

“The first edition of this book was very good; the second is even better, and more versatile. This text remains one of the most attractive sources available from which to learn elementary Lie group theory, and is highly recommended.” (Mark Hunacek, The Mathematical Gazette, Vol. 101 (551), July, 2017)


Video

Table of contents (14 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-13467-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-319-13466-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 4, 2016
  • ISBN 978-3-319-37433-8
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Lie Groups, Lie Algebras, and Representations
Book Subtitle
An Elementary Introduction
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
222
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-13467-3
DOI
10.1007/978-3-319-13467-3
Hardcover ISBN
978-3-319-13466-6
Softcover ISBN
978-3-319-37433-8
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XIII, 453
Number of Illustrations and Tables
7 b/w illustrations, 72 illustrations in colour
Topics