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

摘要

m-Dimensional noncommutative 3-Lie algebras with β(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.