Complex and Kähler structures on hom-Lie algebras

Abstract

(Almost) Complex and Hermitian structures on hom-Lie algebras are introduced and some examples of these structures are presented. We study the complexification of hom-Lie algebras. Also, the notion of Kähler hom-Lie algebras is introduced and then using a Kähler hom-Lie algebra, we present a phase space. Finally, we describe all two-dimension non-abelian Kähler hom-Lie algebra and also it is shown that there does not exist a non-abelian Kähler proper hom-Lie algebra of dimension two.