  In this paper, we introduce the notion of algebras of quotients of Hom-Lie
algebras and investigate some properties which can be lifted from a Hom-Lie
algebra to its algebra of quotients. We also give some necessary and sufficient
conditions for Hom-Lie algebras having algebras of quotients. We also examine
the relationship between a Hom-Lie algebra and the associative algebra
generated by inner derivations of the corresponding Hom-Lie algebra of
quotients. Moreover, we introduce the notion of dense extensions and get a
proposition about Hom-Lie algebras of quotients via dense extensions.
