Matrix Groups: An Introduction to Lie Group Theory

Baker, A. (2002) Matrix Groups: An Introduction to Lie Group Theory. Series: Springer undergraduate mathematics series. Springer: London, UK. ISBN 9781852334703

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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 tions. 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.

Item Type:Books
Glasgow Author(s) Enlighten ID:Baker, Dr Andrew
Authors: Baker, A.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
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