Non-commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras. (English) Zbl 1394.17007

Makhlouf, A.; Amri, A.

J. Gen. Lie Theory Appl. 9, No. 1, Article ID 1000221, 8 p. (2015).

Summary: 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 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.

MSC:

17A40	Ternary compositions
17A60	Structure theory for nonassociative algebras

Keywords:

Hom-Nambu Poisson algebra; ternary Nambu Poisson; noncommutative ternary; \(n\)-ary