Lie Groups pp 175-181 | Cite as


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


In this chapter, we will take a closer look at the groups SO(N) and their double covers, Spin(N). We assume that N ≥ 3 and that N = 2n + 1 or 2n. The group Spin(N) was constructed at the end of Chapter 13 as the universal cover of SO(N). Since we proved that πl (SO(N)) ≅ ℤ/2ℤ, it is a double cover. In this chapter, we will construct and study the interesting and important spin representations of the group Spin(N). We will also show how to compute the center of Spin(N).


Weyl Group Short Exact Sequence Double Cover Semidirect Product Clifford Algebra 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

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

Personalised recommendations