  The main purpose of this paper is to study non-commutative ternary
Nambu-Poisson algebras and their Hom-type version. We provide construction
results dealing with tensor product and direct sums of two (non-commutative)
ternary (Hom-)Nambu-Poisson algebras. Moreover, we explore twisting principle
of (non-commutative) ternary Nambu-Poisson algebras along with an algebra
morphism that lead to construct (non-commutative) ternary Hom-Nambu-Poisson
algebras. Furthermore, we provide examples and a 3-dimensional classification
of non-commutative ternary Nambu-Poisson algebras.
