  Complex and Hermitian structures on hom-Lie algebras are introduced and some
examples of these structures are presented. Also, it is shown that there not
exists a proper complex (Hermitian) home-Lie algebra of dimension two. Then
using a hom-left symmetric algebra, a phase space is provided and then a
complex structure on it, is presented. Finally, the notion of Kahler hom-Lie
algebra is introduced and then using a Kahler hom-Lie algebra, a phase space is
constructed.
