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 L...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.展开更多
基金Supported by NNSF of China(Nos.11771069 and 12071405).
文摘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.
