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

Abstract

The aim of this paper is to generalise the construction of $n$-ary Hom-Lie bracket by means of an $(n-2)$-cochain of given Hom-Lie algebra to super case inducing a $n$-Hom-Lie superalgebras. We study the notion of generalized derivation and Rota-Baxter operators of $n$-ary Hom-Nambu and $n$-Hom-Lie superalgebras and their relation with generalized derivation and Rota-Baxter operators of Hom-Lie superalgebras. We also introduce the notion of $3$-Hom-pre-Lie superalgebras which is the generalization of $3$-Hom-pre-Lie algebras.

References in corpus (17)

• Deformations of Lie Algebras using $\sigma$-derivations
• On Foundation of the Generalized Nambu Mechanics
• Representations of hom-Lie algebras
• Hom-algebras and homology
• n-ary algebras: a review with applications
• On the Quantization of Nambu Brackets
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Quasi-Lie structure of twisted derivations of Laurent polynomials
• Generalized derivations of (color) n-ary algebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• A Hom-associative analogue of n-ary Hom-Nambu algebras
• On Structure and Central Extensions of $(n+1)$-Lie Algebras Induced by $n$-Lie Algebras
• Rota-Baxter bisystems and covariant bialgebras
• Curved O-operator systems
• Cohomology of Hom-Leibniz and $n$-ary Hom-Nambu-Lie superalgebras

Cited by in corpus (3)

• Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras
• Non-degenerate Killing forms on Hom-Lie superalgebras
• Hom-pre-Malcev and Hom-M-Dendriform algebras