Complex and Kähler structures on hom-Lie

Abstract

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