Representations of 3-Dimensional Simple Multiplicative Hom-Lie Algebras.

The aim of this paper is to study representations of 3-dimensional simple multiplicative Hom-Lie algebras (g; [-,- ]; α) (whose structure is of A₁-type). In this paper we can see that a finite dimensional representation of (g; [[-,- ]; α) is not always completely reducible, and a representation of (g; [-,-]; α) is irreducible if and only if it is a regular Lie-type representation. [ABSTRACT FROM AUTHOR]