Hyponilpotent Ideals Of N-lie Algebras

The properties of hyponilpotent ideals of n-Lie algebras, and the structur of inner derivation algebras of solvable 3-Lie algebras possessing a maximal hypo-nilpotent ideal are studied. The results that nilradial of an n-Lie algebra is the proper subalgebra of every maximal hypo-nilpotent ideal and for every a solvable but nonilpotnt n-Lie algebra there exist hypo-nilpotent ideals are proved. The relationship between the dimensions of an n-Lie algebra and its maximal hypo-nilpotent ideals is provided. At last, the structure of inner derivation algebras of solvable 3-Lie algebras with the maximal hypo-nilpotent ideal N is discussed.The paper consists of four sections. The back ground and development of n-Lie algebras are introduced in section 1. Some definitions and notions used in the paper are provided in section 2. The properties of hypo-nilpotent ideals of n-Lie algebras are studied in section 3. The structure of inner derivation algebras of solvable 3-Lie algebras with the maximal hyponilpotent idwal N are discussed in the last section.