Three Ideals of Lie Superalgebras
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.
2012 ◽
Vol 148
(5)
◽
pp. 1561-1592
◽
2016 ◽
Vol 68
(2)
◽
pp. 258-279
◽
Keyword(s):
1994 ◽
Vol 05
(03)
◽
pp. 389-419
◽
1987 ◽
Vol 28
(3)
◽
pp. 310-327
◽
Keyword(s):
2018 ◽
Vol 17
(11)
◽
pp. 1850212
2017 ◽
Vol 16
(03)
◽
pp. 1750050
Keyword(s):