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

2021/12/28 by Taoufik Chtioui, Chtioui, Taoufik, Atef Hajjaji +5
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2112.14290

openalex publication_date 2021/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Related

• 3-L-dendriform algebras and generalized derivations
• Pre-Lie algebras in positive characteristic
• Degenerations of pre-Lie algebras
• From pre-Lie bialgebras to phase spaces of Lie algebras: a categorical correspondence
• On Structure and Central Extensions of (n+1)-Lie Algebras Induced by n-Lie Algebras