Advertisement

Lie Groups and Lie Algebras

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

Abstract

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.

Keywords

Vector Space Heisenberg Group Closed Subgroup Complex Vector Space Coadjoint Representation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations