度量Hom-3-李代数的结构

Structure of metric Hom-3-Lie algebras

定义了度量Hom-3-李代数及乘法度量Hom-3-李代数,并对其基本结构进行了研究.证明了任意一个度量Hom-3-李代数都可以分解为其不可约理想的直和,且每个不可约理想分别是不可约的度量Hom-3-李代数.利用度量3-李代数的代数同态及型心中的元素分别构造了度量Hom-3-李代数及乘法度量Hom-3-李代数.

The definitions of the metric Hom-3-Lie algebra and the metric multiplicative Hom-3-Lie algebra are introduced, and their basic structures are studied.It is proved that every metric Hom-3-Lie algebra can be decomposed into the direct sum of non-degenerate irreducible ideals which are irreducible metric Hom-3-Lie algebra.And metric Hom-3-Lie algebra and the metric multiplicative Hom-3-Lie algebra are constructed by the metric Hom-3-Lie algebras.