  In this paper, we study the cohomology theory of Hom-Lie triple systems
generalizing the Yamaguti cohomology theory of Lie triple systems. We introduce
the central extension theory for Hom-Lie triple systems and show that there is
a one-to-one correspondence between equivalent classes of central extensions of
Hom-Lie triple systems and the third cohomology group. We develop the
1-parameter formal deformation theory of Hom-Lie triple systems, and prove that
it is governed by the cohomology group.
