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

Articles in Press

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Sciences, Arak University, 85156-8-8349, Po.Box: 879, Arak, Iran.

10.22034/as.2024.20876.1689

Abstract

This paper aims to study the double derivation algebra ${\mathcal D}(\mathcal{L})$ of $n$-Hom-Lie color algebra $\mathcal{L}$ and describe the relation between ${\mathcal D}(\mathcal{L})$ and the usual derivation Hom-Lie color algebra $Der(\mathcal{L})$. We prove that the inner derivation algebra $Inn(\mathcal{L})$ is an ideal of the double derivation algebra ${\mathcal D}(\mathcal{L})$. We also show that if $\mathcal{L}$ is a perfect $n$-Hom Lie color algebra with certain constraints on the base field, then the centralizer of $Inn(\mathcal{L})$ in ${\mathcal D}(\mathcal{L})$ is trivial. In addition, we obtain that for every centerless perfect $n$-Hom-Lie color algebra $\mathcal{L}$, the triple derivations of the derivation algebra $Der(\mathcal{L})$ are exactly the derivations of $Der(\mathcal{L})$.

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References

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Algebraic Structures and Their Applications

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Available Online from 03 December 2024

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