Abstract
The goal of this work is to introduce the notion of 3-Hom-L-dendriform algebras which is the dendriform version of 3-Hom-Lie-algebras. They can be also regarded as the ternary analogous of Hom-L-dendriform algebras. We give the representation of a 3-Hom-pre-Lie algebra. Moreover, we introduce the notion of Nijenhuis operators on a 3-Hom-pre-Lie algebra and provide some constructions of 3-Hom-L-dendriform algebras in term of Nijenhuis operators. Parallelly, we introduce the notion of a product and complex structures on a 3-Hom-L-dendriform algebras and there are also four types special integrability conditions.
Acknowledgment
The authors would like to thank the referee for valuable comments and suggestions on this article.
Disclosure statement
No potential conflict of interest was reported by the author(s).