Overview
- Only introduction to Lie group theory aimed at the undergraduate
- Discusses applications in mathematics and physics
- Provides a self-contained introduction to Lie groups and serves as a foundation for a more abstract course in Lie theory and differential geometry
- Uses solved examples and exercises to build the reader's confidence in a subject that can be difficult to tackle
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (12 chapters)
-
Front Matter
-
Matrix Groups as Lie Groups
-
Front Matter
-
-
Compact Connected Lie Groups and their Classification
-
Front Matter
-
-
Back Matter
Keywords
About this book
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)
Authors and Affiliations
Bibliographic Information
Book Title: Matrix Groups
Book Subtitle: An Introduction to Lie Group Theory
Authors: Andrew Baker
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-1-4471-0183-3
Publisher: Springer London
-
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London 2002
Softcover ISBN: 978-1-85233-470-3Published: 09 November 2001
eBook ISBN: 978-1-4471-0183-3Published: 06 December 2012
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XI, 330
Topics: Topological Groups, Lie Groups, Linear and Multilinear Algebras, Matrix Theory, Differential Geometry, Theoretical, Mathematical and Computational Physics, Group Theory and Generalizations