Journal of East China Normal University(Natural Science) ›› 2022, Vol. 2022 ›› Issue (2): 1-8.doi: 10.3969/j.issn.1000-5641.2022.02.001

• Mathematics •     Next Articles

Infinite dimensional 3-Pre-Lie algebras

Ruipu BAI1,2,*(), Shan LIU1,2   

  1. 1. College of Mathematics and Information Science, Hebei University, Baoding Hebei 071002, China
    2. Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province, Hebei University, Baoding Hebei 071002, China
  • Received:2020-10-21 Online:2022-03-25 Published:2022-03-28
  • Contact: Ruipu BAI E-mail:bairuipu@hbu.edu.cn

Abstract:

Constructing 3-Pre-Lie algebras has always been a difficult problem; until now, there have been very few examples of 3-Pre-Lie algebras. In this paper, we use homogenous Rota-Baxter operators of weight zero on the infinite dimensional 3-Lie algebra $A_{\omega}=\langle L_m | m\in {\mathbb{Z}}\rangle$ to construct 3-Pre-Lie algebras $B_k,~0\leqslant k\leqslant 4$ , and we subsequently discuss the structure. It is shown that $B_2$ and $B_4$ are non-isomorphic simple 3-Pre-Lie algebras, $B_1$ is an indecomposable 3-Pre-Lie algebra with infinitely many one-dimensional ideals, and $B_3$ is an indecomposable 3-Pre-Lie algebra with finitely many ideals.

Key words: 3-Pre-Lie algebras, 3-Lie algebras, homogenous Rota-Baxter operator

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