保积Hom-δ-李超三系的拟导子和型心

Quasiderivation and Centroid of Multiplicative Hom-δ-Lie Supertriple Systems

首先给出Hom-δ-李超三系T的概念,证明T的广义导子之集、拟导子之集、导子之集Der(T)、中心导子之集ZDer(T)、拟型心QC(T)和型心C(T)均为李超代数.其次,证明中心导子代数和型心代数都是Der(T)的理想,且ZDer(T)=C(T)∩Der(T).若T的中心为零,则[C(T),QC(T)]={0}.

Firstly,we give the notion of Hom-δ-Lie supertriple systems and prove that generalized derivations,quasiderivations,derivations Der(T),central derivations ZDer(T),quasicentroids QC(T)and centroids C(T)are Lie superalgebras in a Hom-δ-Lie supertriple system T.Secondly,we prove that ZDer(T)and C(T)are ideals of Der(T)and ZDer(T)=C(T)∩Der(T).If T is centerless,then[C(T),QC(T)]={0}.