吉林大学学报（理学版）2017，Vol.55Issue(4)：784-790,7.DOI:10.13413/j.cnki.jdxblxb.2017.04.05
δ-李超三系线性变换构成的六类代数
Six Types of Algebras Generated by Linear Transformationsof a δ-Lie Supertriple System
摘要
Abstract
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.关键词
李超三系/δ-李超三系/广义导子/拟型心Key words
Lie supertriple system/δ-Lie supertriple system/generalized derivation/quasicentroids分类
数理科学引用本文复制引用
邢晋,牛艳君,陈良云..δ-李超三系线性变换构成的六类代数[J].吉林大学学报（理学版）,2017,55(4):784-790,7.基金项目
国家自然科学基金(批准号:11471090 （）
11171055). （）
