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The paper studies nilpotent -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for -Lie superalgebras which is a generalization of those for -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent -Lie superalgebras and obtain several sufficient conditions for an -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal and the...
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