Lie Groups and Algebras: Matrix Approach

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


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 \( \delta R = \dot R(0) = (_1^0{}_0^{ - 1}) \).


Tangent Vector Parameter Group Matrix Approach Infinitesimal Generator Jordan Canonical Form 
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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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