Matrix Groups An Introduction to Lie Group Theory

Matrix Groups An Introduction to Lie Group Theory / by Andrew Baker.

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 (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: London : Springer London : Imprint: Springer, 2002.
Edition:1st ed. 2002.
Series:Springer Undergraduate Mathematics Series,
Springer eBook Collection.
Subjects:
Topological groups.
Lie groups.
Matrix theory.
Algebra.
Differential geometry.
Mathematical physics.
Group theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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