Simple Roots and Weyl Groups

G.Manjula

doi:https://doi.org/10.14445/22315373/IJMTT-V40P535

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 40 | Number 4 | Year 2016 | Article Id. IJMTT-V40P535 | DOI : https://doi.org/10.14445/22315373/IJMTT-V40P535

Simple Roots and Weyl Groups

G.Manjula

Abstract

Its origins in the theory of Lie algebras are introduced, and then an axiomatic definition is provided. Simple roots, Bases, Weyl groups, and the transitive action of the latter on the former are explained and proven, respectively.

Keywords

Simple roots, Bases, Weyl groups.

References

[1] A. Baker, Matrix Groups: An Introduction to Lie Group Theory, Springer, 2002.
[2] N. Bourbaki, Lie Groups and Lie Algebras (Chapters 4-6), Springer, 2002.
[3] K. Erdmann and M.J. Wildon, Introduction to Lie algebras, Springer Under-graduate Mathematics Series. Springer-Verlag London Ltd., London, 2006.
[4] B.C. Hall, Lie Groups, Lie Algebras, and Representations, An Elementary Introduction, Springer, 2003.
[5] J.E. Humphrey, Introduction to Lie Algebras and Representation Theory, Springer, 1972.
[6] N. Jacobson, Lie Algebras, John Wiley & Sons, 1962 [7] W. Rossmann, Lie Groups: An Introduction through Linear Groups, Oxford University Press, 2002.
[8] B. Simon, Representations of Finite and Compact Groups, American Mathematical Society, 1996.

Citation :

G.Manjula, "Simple Roots and Weyl Groups," International Journal of Mathematics Trends and Technology (IJMTT), vol. 40, no. 4, pp. 276-280, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V40P535