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arXiv · 2112.14290

On $n$-pre-Lie algebras and dendrification of $n$-Lie algebras

Taoufik Chtioui·Atef Hajjaji·Sami Mabrouk·Abdenacer Makhlouf
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Abstract

The main purpose of this paper is to introduce the notion of $n$-L-dendriform algebra which can be seen as a dendrification of $n$-pre-Lie algebras by means of $\mathcal{O}$-operators. We investigate the representation theory of $n$-pre-Lie algebras and provide some related constructions. Furthermore, we introduce the notion of phase space of a $n$-Lie algebra and show that a $n$-Lie algebra has a phase space if and only if it is sub-adjacent to a $n$-pre-Lie algebra. Moreover, we present a procedure to construct $(n + 1)$-pre-Lie algebras from $n$-pre-Lie algebras equipped with a generalized trace function.

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Taoufik Chtioui, Atef Hajjaji, Sami Mabrouk, Abdenacer Makhlouf. 2021-12-28. On $n$-pre-Lie algebras and dendrification of $n$-Lie algebras. https://arxiv.org/abs/2112.14290

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