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Lie Groups and Algebras: Matrix Approach

  • D. H. Sattinger
  • O. L. Weaver
Part of the Applied Mathematical Sciences book series (AMS, volume 61)

Abstract

The Lie algebra g of a Lie group G is by definition the tangent space to G (considered as an analytic manifold) at the identity. When G is a matrix Lie algebra the elements of g may be obtained by differentiating curves of matrices. For example, the curve in SO(2) given by
$$ R(\theta ) = (_{\sin \theta }^{\cos \theta }{}_{\cos \theta }^{ - \sin \theta }) $$
has as its tangent vector at the identity \( \delta R = \dot R(0) = (_1^0{}_0^{ - 1}) \).

Keywords

Tangent Vector Parameter Group Matrix Approach Infinitesimal Generator Jordan Canonical Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • D. H. Sattinger
    • 1
  • O. L. Weaver
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of PhysicsKansas State UniversityManhattanUSA

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