辛三代数的结构群和结构代数

Structure Group and Structure Algebra of the Symplectic Ternary Algebras

在文献[1]中,FAULKNERJR和FERRARJC引入了辛三代数的定义,建立了它与李三系、李代数的联系,并且讨论了它的半单性、迹型和可解性.在文献[2]中,MEYBERGK定义了Jordan三系的结构群和结构代数.本文给出了辛三代数的结构群和结构代数的定义,并得到了几个重要结果:1)辛三代数S的结构群和与S相关联的李三系的自同构群的一个子群同构;2)辛三代数S的结构代数的一个子代数和与S相关联的李三系的导子代数的一个子代数同构;3)辛三代数S的结构代数的一个σ-不动点集与S的导子代数同构;4)辛三代数S的结构群对其内结构代数的一个作用是稳定的.

In the literature[1],FAULKNER J R and FEERRAR J C gave the definition of symplectic ternary algebra and constructed the relations between it and Lie triple system,Lie algebra,then they studied its semi-simplicity,traces and solvability.In the literature[2],MEYBERG K defined the structure groups and the structure algebras of Jordan triple systems.The definitions of symplectic ternary algebras' structure groups and structure algebras are given in the present paper,and some important conculusions are obtained:1)The structure group of a symplectic ternary algebra is isomorphic to the automorphism group of the Lie triple system associated with it ;2)The structure algebra of a symplectic ternary algebra is isomorphic to a subalgebra of the derivation algebra of the Lie triple system associated with it;3)One of the σ-invariant point sets of a symplectic ternary algebra is isomorphic to the derivation algebra of it ;4)One of the actions of the structure group of a symplectic ternary algebra on its inner structure algebra is invariant.