Representations of 3-dimensional simple multiplicative Hom-Lie algebras (Q2248479)

Summary: The aim of this paper is to study representations of 3-dimensional simple multiplicative Hom-Lie algebras \((g;[\cdot,\cdot];\alpha)\) (whose structure is of \(A_{1}\)-type). In this paper we can see that a finite dimensional representation of \((g;[\cdot,\cdot];\alpha)\) is not always completely reducible, and a representation of \((g;[\cdot,\cdot];\alpha)\) is irreducible if and only if it is a regular Lie-type representation.