Lie Groups and Lie Algebras

  • Pr Yvette Kosmann-Schwarzbach
  • Stephanie Frank Singer
Part of the Universitext book series (UTX)


We restrict ourselves to the study of linear Lie groups, that is, to closed subgroups of GL(n,ℝ), for an integer n, in other words, to groups of real matrices. We adopt the convention, introduced in Chapter 1, of calling such a group simply a Lie group. We shall show that to each Lie group there corresponds a Lie algebra. For ease of exposition, we start by defining Lie algebras, and return later to the study of groups.


Vector Space Heisenberg Group Closed Subgroup Complex Vector Space Coadjoint Representation 
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Copyright information

© Springer-Verlag New York 2010

Authors and Affiliations

  • Pr Yvette Kosmann-Schwarzbach
    • 1
  • Stephanie Frank Singer
    • 2
  1. 1.Ecole PolytechniquePalaiseauFrance
  2. 2.PhiladelphiaUSA

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