Three Ideals of Lie Superalgebras  

作　　者：Xiaodong Zhao Liangyun Chen 

机构地区：[1]School of Mathematics and Statistics,Northeast Normal University Changchun 130024,China [2]School of Mathematics and Statistics,Yili Normsd University Yining,Xinjiang 835000,China

出　　处：《Algebra Colloquium》2022年第1期143-150,共8页代数集刊（英文版）

基　　金：Supported by NNSF of China(Nos.11771069 and 12071405).

摘　　要：We define perfect ideals,near perfect ideals and upper bounded ideals of a finite-dimensional Lie superalgebra,and study the properties of these three kinds of ideals through their relevant sequences.We prove that a Lie superalgebra is solvable if and only if its maximal perfect ideal is zero,or its quotient superalgebra by the maximal perfect ideal is solvable.We also show that a Lie superalgebra is nilpotent if and only if its maximal near perfect ideal is zero.Moreover,we prove that a nilpotent Lie superalgebra has only one upper bounded ideal,which is the nilpotent Lie superalgebra itself.

关 键 词：Lie superalgebras perfect ideals near perfect ideals upper bounded ideals SOLVABLE NILPOTENT 

分 类 号：O15[理学—数学]