The constructions and deformations of Nijenhuis operators on 3-Hom-Lie algebras
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In this paper, we study Nijenhuis operators on 3-Hom-Lie algebras and provide some examples. Next, we give various constructions of Nijenhuis operators according to constructions of 3-Hom-Lie algebras. Furthermore, we define a cohomology of Nijenhuis operators on 3-Hom-Lie algebras with coefficients in a suitable representation. Finally, as an application, we study formal deformations of Nijenhuis operators that are generated by the above-defined cohomology.
Abstract
In this paper, we study Nijenhuis operators on 3-Hom-Lie algebras and provide some examples. Next, we give various constructions of Nijenhuis operators according to constructions of 3-Hom-Lie algebras. Furthermore, we define a cohomology of Nijenhuis operators on 3-Hom-Lie algebras with coefficients in a suitable representation. Finally, as an application, we study formal deformations of Nijenhuis operators that are generated by the above-defined cohomology.