Lie Groups pp 45-49 | Cite as

Left-Invariant Vector Fields

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)


To recapitulate, a Lie group is a differentiable manifold with a group structure in which the multiplication and inversion maps G × G ⟶ G and G ⟶ G are smooth. A homomorphism of Lie groups is a group homomorphism that is also a smooth map.


Vector Field Group Structure Smooth Manifold Group Homomorphism Real Vector Space 
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.


  1. 25.
    T. Bröcker and T. tom Dieck. Representations of Compact Lie Groups, volume 98 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1985.Google Scholar
  2. 105.
    A. Knapp. Lie groups, Lie algebras, and Chomology, volume 34 of Mathematical Notes. Princeton University Press, Princeton, NJ, 1988.Google Scholar
  3. 106.
    A. Knapp. Lie Groups Beyond an Introduction, volume 140 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, second edition, 2002.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

Personalised recommendations