The Determination of a Class of Solvable Multiplicative Hom-Lie Algebras

Abstract

By the deformation of nilpotent Lie algebra Q2nand its automorphism α, nilpotent multiplicative Hom-Lie algebra (Q2n,[,]',α) is obtained. All finite-dimensional indecomposable solvable multiplicative Hom-Lie algebras (L,[,]',σ), having the nilpotent multiplicative Hom-Lie algebra (Q2n,[,]',α) as the nilradical, are studied and determined. It shows that the dimension of Hom-Lie algebra (L,[,]',σ) is dimQ2n+1.