A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.
References
[1]
Roberts, B. (2018-2019) Lie Algebras. University of Idaho, Moscow. https://www.webpages.uidaho.edu/~brooksr/liealgebraclass.pdf
Hasic, A. (2021) Introduction to Lie Algebras and Their Representations. Advances in Linear Algebra & Matrix Theory, 11, 67-91. Introduction to Lie Algebras and Their Representations (scirp.org) https://doi.org/10.4236/alamt.2021.113006
[4]
Onishchik, A.L. and Vinberg, E.B. (Eds.) (1990) Lie Groups and Lie Algebras III. Structure of Lie Groups and Lie Algebras. VINITI, Moscow. https://books.google.me/books?id=l8nJCNiIQAAC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
[5]
Wikipedia (2023) Root System. https://en.wikipedia.org/wiki/Root_system