具有β(L)=m-3的m-维非交换3-李代数的分类

The Classification of m-Dim Noncommutative 3-Lie Algebras with β(L)=m-3

对特征零域F上具有β(L)=m-3的m-维非交换3-李代数的结构进行了分类,且给出了每一类3-李代数的具体乘法结构.证明了满足β(L)=m-3且中心含在导代数的非交换3-李代数的维数小于等于11,大于等于5,且导代数维数等于1时的3-李代数仅有两类,导代数维数等于2时有24类.

m-Dimensional noncommutative 3-Lie algebras withβ(L)=m-3 over a field of characteristic zero are classified,and the exact multiplications are provided.It is proved that if the center of L is contained in L^(1),then 5≤m≤11.And in the cases dim L^(1)=1 and 2,there exist only 2 classes and 24 classes non-isomorphic 3-Lie algebras,respectively.