$3$-L-dendriform algebras and generalized derivations

Abstract

The main goal of this paper is to introduce the notion of $3$-L-dendriform algebras which are the dendriform version of $3$-pre-Lie algebras. In fact they are the algebraic structures behind the $\mathcal{O}$-operator of $3$-pre-Lie algebras. They can be also regarded as the ternary analogous of L-dendriform algebras. Moreover, we study the generalized derivations of $3$-L-dendriform algebras. Finally, we explore the spaces of quasi-derivations, the centroids and the quasi-centroids and give some properties.

arXiv admin note: text overlap with arXiv:1604.05996, arXiv:1711.08381, arXiv:1306.3046 by other authors