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Six Types of Algebras Generated by Linear Transformationsof a δ-Lie Supertriple System
XING Jin, NIU Yanjun, CHEN Liangyun
Journal of Jilin University Science Edition. 2017, 55 (04):
784-790.
We considered six types of algebras generated by linear transformations of a δ-Lie supertriple system T: the derivation algebra Der(T), the quasiderivation algebra QDer(T), the generalized derivation algebra GDer(T), the central derivation algebra ZDer(T), the centroid algebra C(T), and the quasicentroid algebra QC(T). We first proved that ZDer(T) was an ideal of Der(T) and ZDer(T)Der(T)QDer(T)GDer(T)End(T), then obtained that [Der(T),C(T)]C(T), [QDer(T),QC(T)]QC(T), [QC(T),QC(T)\]QDer(T), QDer(T)+QC(T)=GDer(T) and[C(T),QC(T)]End(T,Z(T)). Moreover, we proved that if a δ-Lie supertriple system was decomposable, then its generalized derivation algebra, quasiderivation algebra, centroid algebra, and quasicentroid algebra also had corresponding decomposition, respectively.
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