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Matrix Groups : an Introduction to Lie Group Theory /

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 o...

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Bibliographic Details
Main Author: Baker, Andrew
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: London : Springer London, 2002.
Series:Springer undergraduate mathematics series.
Subjects:
Mathematics.
Group theory.
Matrix theory.
Topological groups.
Global differential geometry.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Part I. Basic Ideas and Examples: Real and Complex Matrix Groups. Exponentials, Differential Equations and One Parameter Subgroups. Tangent Spaces and Lie Algebras. Algebras, Quaternions, and Symplectic Groups. Clifford Algebras and Spinor Groups. Lorentz Groups
  • Part II. Matrix Groups as Lie Groups: Lie groups. Homogeneous Spaces. Connectivity of Matrix Groups
  • Part III. Compact Connected Lie Groups and their Classification: Maximal Tori in Compact Connected Lie Groups. Semi-simple Factorization. Roots systems, Weyl Groups and Dynkin Diagrams
  • Bibliography
  • Index.