Multiplicative n-Hom-Lie color algebras

Abstract

The purpose of this paper is to generalize some results on n-Lie algebras and n-Hom-Lie algebras to n-Hom-Lie color algebras. Then we introduce and give some constructions of n-Hom-Lie color algebras.

Double derivations of $n-$Hom-Lie color algebras

“…Let us begin with some necessary important basic definitions and notations on graded spaces, algebras and n−Hom-Lie color algebras used in other sections. For a detailed discussion of this subject, we refer the reader to the literature [6].…”

“…If L 1 = L, then L is called a perfect n−Hom-Lie color algebra. The center of an n−Hom-Lie color algebra L is denoted by Z(L) = {x ∈ L : [x, L, ..., L] = 0} which is a Hom-ideal of L (see Theorem 2.16 in [6]). For a subset S of L, the centralizer of S in L is defined by…”

“…We also have that (Der(L), [., . ], α = D • α, ǫ) is a Hom-Lie color algebra (see Proposition 5.7 in [6]).…”

Hom-pre-Malcev and Hom-M-Dendriform algebras

“…Since the pioneering works [18,[29][30][31][32]47], Hom-algebra structures have developed in a popular broad area with increasing number of publications in various directions. Hom-algebra structures include their classical counterparts and open new broad possibilities for deformations, extensions to Hom-algebra structures of representations, homology, cohomology and formal deformations, Hommodules and hom-bimodules, Hom-Lie admissible Hom-coalgebras, Hom-coalgebras, Hom-bialgebras, Hom-Hopf algebras, L-modules, L-comodules and Hom-Lie quasibialgebras, n-ary generalizations of biHom-Lie algebras and biHom-associative algebras and generalized derivations, Rota-Baxter operators, Hom-dendriform color algebras, Rota-Baxter bisystems and covariant bialgebras, Rota-Baxter cosystems, coquasitriangular mixed bialgebras, coassociative Yang-Baxter pairs, coassociative Yang-Baxter equation and generalizations of Rota-Baxter systems and algebras, curved Ooperator systems and their connections with tridendriform systems and pre-Lie algebras, BiHom-algebras, BiHom-Frobenius algebras and double constructions, infinitesimal biHom-bialgebras and Hom-dendriform D-bialgebras, and category theory of Homalgebras [2,3,[5][6][7][8][9][10][11][12]15,16,[19][20][21][22][23][24]29,[32][33][34][37][38][39][40]42,45,[48][49][50]…”

Generalized Derivations and Rota-Baxter Operators of $n$-ary Hom-Nambu Superalgebras

“…Generalizations of derivations in connection with extensions and enveloping algebras of Hom-Lie color algebras have been considered in [12,13,31]. Generalized derivations of mul-tiplicative n-ary Hom-Ω color algebras have been studied in [36].…”