VERY GOOD: The book is in very good condition, showing only slight signs of use and wear (namely, a mark along the outer page edge and slightly bent corners). The pages are clean of writing and the binding is tight. This book was printed on acid-free paper. NOTE: British spelling.
Product Details
From the back cover: "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."
BRIEF CONTENTS
Part I. Basic Ideas and Examples
1. Real and Complex Matrix Groups
2. Exponentials, Differential Equations and One-parameter Subgroups
3. Tangent Spaces and Lie Algebras
4. Algebras, Quaternions and Quaternionic Symplectic Groups
5. Clifford Algebras and Spinor Groups
6. Lorentz Groups
Part II. Matrix Groups as Lie Groups
7. Lie Groups
8. Homogeneous Spaces
9. Connectivity of Matrix Groups
Part III. Compact Connected Lie Groups and Their Classification
10. Maximal Tori in Compact Connected Lie Groups
11. Semi-simple Factorisation
12. Roots Systems, Weyl Groups and Dynkin Diagrams
