Pembentukan Representasi Adjoin pada Aljabar Lie

Algebra is a branch of mathematics that can provide understanding in solving problems. This research discusses one form of algebra, namely Lie algebra. Where Lie algebra 𝗀 is a vector space over the field 𝔽 equipped with a bilinear mapping equipped by a commutator operation commonly called the Lie bracket operation denoted [−, −] from 𝗀 × 𝗀 to 𝗀 if it satisfies the anti-symmetry axiom and satisfies Jacobi Identity. One model of Lie algebra is the set of all linear operators of a vector space 𝑉 denoted by 𝑔𝑙(𝑉). In addition, one of the discussions related to Lie algebra in this research is representation theory. Lie algebra uses representation theory with the aim of simplifying abstract algebraic problems into linear algebra by presenting each of its members in the form of linear mappings on vector spaces. There are various forms of representation theory in Lie algebra, one of which is adjoin representation. And this adjoin representation is formed from a derivation and Lie homomorphism. The purpose of this research is to find out how the formation of adjoin representation on Lie algebra. This research uses a qualitative method, where the method applies a way to collect data or library materials as a reference in the form of articles, journals, and even books related to Lie algebra.