  A Hom-algebra structure is a multiplication on a vector space where the
structure is twisted by a homomorphism. The structure of Hom-Lie algebra was
introduced by Hartwig, Larsson and Silvestrov and extended by Larsson and
Silvestrov to quasi-hom Lie and quasi-Lie algebras. In this paper we introduce
and study Hom-associative, Hom-Leibniz, and Hom-Lie admissible algebraic
structures which generalize the well known associative, Leibniz and Lie
admissible algebras. Also, we characterize the flexible Hom-algebras in this
case. We also explain some connections between Hom-Lie algebras and Santilli's
isotopies of associative and Lie algebras.
