Matrix groups : an introduction to Lie group theory

Author(s)

    • Baker, Andrew

Bibliographic Information

Matrix groups : an introduction to Lie group theory

Andrew Baker

(Springer undergraduate mathematics series)

Springer, c2002

  • : pbk

Available at  / 36 libraries

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Note

Includes bibliographical reference (p. 323-324) and index

Description and Table of Contents

Description

This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.

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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Details

  • NCID
    BA54754020
  • ISBN
    • 1852334703
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    London
  • Pages/Volumes
    xi, 330 p.
  • Size
    24 cm
  • Parent Bibliography ID
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