  In this article we will build a universal imbedding of a regular Hom- Lie
triple system into a Lie algebra and show that the category of regular Hom-Lie
triple systems is equivalent to a full subcategory of pairs of
$\mathbb{Z}/2\mathbb{Z}$- graded Lie algebras and Lie algebra automorphism,
then finally give some characterizations of this subcategory.
