李超代数Alg(K_(3),ω_(3))上的超双导子及超交换映射

Super-biderivations and super-commuting maps on super Lie algebras Alg(K_(3),ω_(3))

利用超双导子的基本性质,确定李超代数Alg(K_(3),ω_(3))上的超斜对称双导子,证明Alg(K_(3),ω_(3))上的超斜对称双导子都是内导子.得到Alg(K_(3),ω_(3))上的线性超交换映射是标准的.

Using the basic properties of super double derivations,the super-skewsymmetric super-biderivations of the super Lie algebras Alg(K_(3),ω_(3)) are determined,and it is proved that all super-biderivations of the Alg(K_(3),ω_(3)) are inner derivations.Furthermore,it is obtained that the linear super-commuting map of the Alg(K_(3),ω_(3)) is standard.