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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 anoverview of the theory and explore the structure properties such as ideals,center, derived series, solvability, nilpotency, central extensions, and thecohomology.

On $(n+1)$-Hom-Lie Algebras Induced by $n$-Hom-Lie Algebras