Springer Undergraduate Mathematics Series

Matrix Groups

An Introduction to Lie Group Theory

Authors: Baker, Andrew

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eBook $34.99
price for USA (gross)
  • ISBN 978-1-4471-0183-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-85233-470-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter.
The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions.
Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry.

Reviews

From the reviews of the first edition:

MATHEMATICAL REVIEWS

"This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited background…The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate students…To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory."

"This book is an introduction to Lie group theory with focus on the matrix case. … This book can be recommended to students, making Lie group theory more accessible to them." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003)


Table of contents (12 chapters)

  • Real and Complex Matrix Groups

    Baker, Andrew

    Pages 3-43

  • Exponentials, Differential Equations and One-parameter Subgroups

    Baker, Andrew

    Pages 45-65

  • Tangent Spaces and Lie Algebras

    Baker, Andrew

    Pages 67-97

  • Algebras, Quaternions and Quaternionic Symplectic Groups

    Baker, Andrew

    Pages 99-128

  • Clifford Algebras and Spinor Groups

    Baker, Andrew

    Pages 129-156

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4471-0183-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-85233-470-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Matrix Groups
Book Subtitle
An Introduction to Lie Group Theory
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2002
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-0183-3
DOI
10.1007/978-1-4471-0183-3
Softcover ISBN
978-1-85233-470-3
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XI, 330
Topics