A Class Of Sovable 3-Lie Algebras

Solvable 3-Lie algebras and nilpotent 3-Lie algebras are two important classes of 3-Lie algebras, since they play the impotant role in the structural theory of 3-Lie algebras. The paper mainly studied the solvable 3-Lie algebras over the complex field with a spe-cial hyponilpotent ideal. According to the classification of solvable 3-Lie algebras with a 5-dimensional hyponilpotent ideal, it discussed their nilradicals, dimensional sequences DS and CS. And by the multiplication table, the paper studied the the structur of derivation algebras, and gave the concrete expression of derivations. After the system-atically researching, the paper provided the basic foundation for the structural theory of solvabe 3-Lie algebras.The paper consists of four sections. The section 1 introduced the back ground and development of n-Lie algebras. The section 2 recalled some definitions and results which are used in the paper. The section 3 discussed the properties of nilradical and dimensional sequences DS and CS. At the last section, the paper studied the structure of derivation algebras...