Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras

Hom-Lie-Yamaguti Superalgebras

“…Let (A, * , α) be a Hom-superalgebra, that is a K−vector superspace A together with a multiplication " * " and an even linear self-map α. (i) [2] The Hom-superassociator of A is the trilinear map as α : A × A × A → A defined as…”

“…Definition 2.4. [2] Let (A, * , α) be a Hom-superalgebra and n ≥ 0 an integer ( " * " is the binary operation on A). The Hom-superalgebra A n defined by…”

“…In the following, we give some examples of Hom-Lie-Yamaguti superalgebras which are constructed firstly from the example 2.8 in [1] and using Proposition 3.12. In the second from the example 3.2 given in [3] (see also in [2]) and using the Theorem 3.10 via Corollary 3.11 . Then, we obtain some family of Hom-Lie-Yamaguti algebras of dimension 5 and dimension 3 respectively.…”

“…The purpose of this paper is to introduced Hom-type generalization of Lie-Yamaguti superalgebras [12], called Hom-Lie-Yamaguti superalgebras. It is also to extend the notion of an n th −derived (binary) Hom-superalgebras [2] to the one of an n th −derived ternary or binary-ternary Hom-superalgebras and we shown that ternary or binary-ternary superalgebras are closed under the process of taking n th −derived Hom-superalgebras.…”

“…Indeed, they show also that the supercommutator bracket defined using the multiplication in a Hom-associative superalgebra leads naturally to Hom-Lie superalgebras. In [2] the authors introduce the Hom-alternative, Hom-Malcev and Hom-Jordan superalgebras wich are the generalization of Alternative, Malcev and Jordan superalgebras respectively.…”