Author	Baker, Andrew. author
Title	Matrix Groups [electronic resource] : An Introduction to Lie Group Theory / by Andrew Baker
Imprint	London : Springer London : Imprint: Springer, 2002
Connect to	http://dx.doi.org/10.1007/978-1-4471-0183-3
Descript	XI, 330 p. online resource

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

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 -- II. Matrix Groups as Lie Groups -- 7. Lie Groups -- 8. Homogeneous Spaces -- 9. Connectivity of Matrix Groups -- 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 -- Hints and Solutions to Selected Exercises

1. Mathematics
2. Group theory
3. Matrix theory
4. Algebra
5. Topological groups
6. Lie groups
7. Differential geometry
8. Physics
9. Mathematics
10. Topological Groups
11. Lie Groups
12. Linear and Multilinear Algebras
13. Matrix Theory
14. Differential Geometry
15. Theoretical
16. Mathematical and Computational Physics
17. Group Theory and Generalizations