Multiplicative n-Hom-Lie Color Algebras

@article{Bakayoko2017MultiplicativeNC,
  title={Multiplicative n-Hom-Lie Color Algebras},
  author={Ibrahima Bakayoko and Sergei Silvestrov},
  journal={Springer Proceedings in Mathematics \& Statistics},
  year={2017}
}
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. 
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21 Citations
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21 Citations

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References

SHOWING 1-10 OF 80 REFERENCES

Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions

In this article, two classes of Г-graded Witt-type algebras, Lie color and hom-Lie algebras of Witt type, are considered. These algebras can be seen as generalizations of Lie algebras of Witt type.…

On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras

Abstract The purpose of this paper is to study the relationships between an n-Hom-Lie algebra and its induced (n+1)-Hom-Lie algebra. We provide an overview of the theory and explore structure…

Hom-algebras and homology

Classes of $G$-Hom-associative algebras are constructed as deformations of $G$-associative algebras along algebra endomorphisms. As special cases, we obtain Hom-associative and Hom-Lie algebras as…

On classification of n-Lie algebras

In this paper, we prove the isomorphic criterion theorem for (n+2)-dimensional n-Lie algebras, and give a complete classification of (n + 2)-dimensional n-Lie algebras over an algebraically closed…

Representations of Hom-Lie Algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations,…

On Structure and Central Extensions of $(n+1)$-Lie Algebras Induced by $n$-Lie Algebras

The purpose of this paper is to investigate $(n+1)$-Lie algebras induced by $n$-Lie algebras and trace maps. We highlight a comparison of their structure properties (solvability, nilpotency) and the…

Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras

The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced \(3\)-Lie algebras.

Structure of low dimensional n-Lie algebras over a field of characteristic 2☆

Graded quasi-lie algebras of witt type

In this article, we introduce a new class of graded algebras called quasi-Lie algebras of Witt type. These algebras can be seen as a generalization of other Witt-type algebras like Lie algebras of…

Representations and cohomology of n-ary multiplicative Hom–Nambu–Lie algebras

...