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In the present paper, we define the new class of representation on $n$-Liealgebra that is called as generalized representation. We study the cohomologytheory corresponding to generalized representations of $n$-Lie algebras andshow its relation with the cohomology corresponding to the usualrepresentations. Furthermore, we provide the computation for the lowdimensional cocycles.

On the cohomology based on the generalized representations of $n$-Lie Algebras