Matrix Groups: An Introduction to Lie Group Theory (Springer Undergraduate Mathematics Series) - Softcover

Baker, Andrew

Softcover

ISBN 10: 1852334703 ISBN 13: 9781852334703

Publisher: Springer, 2001

Synopsis

This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.

About this title

Review

"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." --Mathematical Reviews

"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

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 1852334703
• ISBN 13: 9781852334703
• Binding: Paperback
• Number of pages: 341