Mathematics

Infinite dimensional 3-Pre-Lie algebras

  • Ruipu BAI ,
  • Shan LIU
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  • 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 date: 2020-10-21

  Online published: 2022-03-28

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.

Cite this article

Ruipu BAI , Shan LIU . Infinite dimensional 3-Pre-Lie algebras[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(2) : 1 -8 . DOI: 10.3969/j.issn.1000-5641.2022.02.001

References

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