Representations of 3-Dimensional Simple Multiplicative Hom-Lie Algebras

Abstract EN

The aim of this paper is to study representations of 3-dimensional simple multiplicative Hom-Lie algebras (?;[·,·];α) (whose structure is of A1-type).

In this paper we can see that a finite dimensional representation of (?;[·,·];α) is not always completely reducible, and a representation of (?;[·,·];α) is irreducible if and only if it is a regular Lie-type representation.