TITLE:
Root Systems Lie Algebras
AUTHORS:
Amor Hasić, Fatih Destović
KEYWORDS:
Lie Algebras, Root Systems, Ways Chambers, Dynkin Diagrams
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.13 No.1,
March
31,
2023
ABSTRACT: 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.