构造3-Pre-李代数一直是一个很困难的问题, 目前关于3-Pre-李代数的例子很少. 利用单无限维3-李代数 $A_{\omega}=\langle L_m~\vert~m\in {\mathbb{Z}}\rangle$ 上所有权为0 的齐性Rota-Baxter 算子, 构造了5类不同构的3-Pre-李代数 $B_k, 0\leqslant k\leqslant4$ , 且对所构造的3-Pre-李代数的结构进行了研究, 证明了 $B_2$ 和 $B_4$ 是2类单3-Pre-李代数, $B_1$ 是具有无限多个1维理想的不可分解3-Pre-李代数, $B_3$ 是具有有限多个理想的不可分解3-Pre-李代数.

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.