无限维3-Pre-李代数

Infinite dimensional 3-Pre-Lie algebras

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_(w)=(L_(m)|m∈Z)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≤k≤4,且对所构造的3-Pre-李代数的结构进行了研究,证明了B_(k)和B_(k)是2类单3-Pre-李代数,B_(k)是具有无限多个1维理想的不可分解3-Pre-李代数,B_(k)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_(w)=(L_(m)|m∈Z) to construct 3-Pre-Lie algebras B_(k),0≤k≤4,and we subsequently discuss the structure.It is shown that B_(k)and B_(k)are non-isomorphic simple 3-PreLie algebras,B_(k)is an indecomposable 3-Pre-Lie algebra with infinitely many one-dimensional ideals,and B;is an indecomposable 3-Pre-Lie algebra with finitely many ideals.