Let π½ be a field of characteristic β 2 and β a finite-dimensional Lie superalgebra over π½. In this article, we study the derivation superalgebra Der(β), the quasiderivation superalgebra QDer(β), and the generalized derivation superalgebra GDer(β) of β, which form a tower Der(β) β QDer(β) β GDer(β) β pl(β), where pl(β) denotes the general linear Lie superalgebra. More precisely, we characterize completely those Lie superalgebras β for which QDer(β) = pl(β). We prove that the quasiderivations of β can be embedded as derivations in a larger Lie superalgebra and, furthermore, when the annihilator of β is equal to zero, we obtain a semidirect sum decomposition of .
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Zhang et al. (2010) studied this question.
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