无限维3-Lie代数F[t,t^(-1)]的结构

Structure of infinite dimensional 3- Lie algebra F[t,t^(-1)]

研究域F上的无限维3-李代数A=F[t,t-1]的结构。当域F的特征分别为零和大于零时,构造A上的一列真理想,并找到A的极大真理想。当域F的特征等于3时,研究商代数A/J的结构,其中J是由向量p(t)=t3-t-3生成的3-李代数A的理想。证明A/J是非可解且非单的6-维3-李代数。

The structure of the 3-Lie algebra A = F[t,t^（-1）] over a field F is studied. A sequence of prop- er ideals and the maximal ideals of A over a field F with chF = 0 and chF 〉 0 are constructed, respective- ly. For the case of chF = 3 , the quotient algebra A/J is discussed, where J is an ideal of the 3-Lie alge- bra A generated by the vectorp（t） = t3 - t -3. It is proved that A/J is an unsolvable and non-simple 3-Lie algebra.