In this paper, we first introduce the concepts of weak -ideals, weak -simple Lie superalgebras and weak -ideals complementability of Lie superalgebras, and investigate some structural properties related to weak -ideals over the fields with characteristics other than , ; Secondly, the necessary and sufficient conditions for a Lie superalgebras to be a weak -simple Lie superalgebras are given. By using ideals, the sufficient and necessary conditions for a weak -ideal of a Lie superalgebra to be its ideal are given, and the necessary and sufficient conditions for its quotient subalgebra to have subideal complement are given; Finally, by using some weak -ideals of a class of Lie superalgebras over fields with characteristic zero, the sufficient conditions for the class of Lie superalgebras to be solvable are given.
Key words
weak -ideals /
weak -simple Lie superalgebras /
weak -ideals complementable /
solvable Lie superalgebras
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References
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