Advertisement

São Paulo Journal of Mathematical Sciences

, Volume 12, Issue 2, pp 246–251 | Cite as

A geometric proof of the Poincaré-Birkhoff-Witt Theorem

  • Michael Eastwood
Article
  • 53 Downloads

Abstract

We use that the n-sphere for \(n\ge 2\) is simply-connected to prove the Poincaré-Birkhoff-Witt Theorem.

Keywords

Poincaré-Birkhoff-Witt Universal enveloping algebra Symmetric group 

Mathematics Subject Classification

16S30 

References

  1. 1.
    Gunning, R.C.: Lectures on Riemann Surfaces. Princeton University Press, Princeton (1966)zbMATHGoogle Scholar
  2. 2.
    Humphreys, J.E.: Reflection Groups and Coxeter Groups. Cambridge University Press, Cambridge (1990)CrossRefGoogle Scholar
  3. 3.
    Jacobson, N.: Lie algebras, Wiley (1962), Dover (1979)Google Scholar

Copyright information

© Instituto de Matemática e Estatística da Universidade de São Paulo 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

Personalised recommendations