Derivations of finite-dimensional modular Lie superalgebras $ \overline{K}(n, m) $

Abstract

This paper is aimed at determining the derivation superalgebra of modular Lie superalgebra $ \overline{K}(n, m) $. To that end, we first describe the $ \mathbb{Z} $-homogeneous derivations of $ \overline{K}(n, m) $. Then we obtain the derivation superalgebra $ Der(\overline{K}) $. Finally, we partly determine the derivation superalgebra $ Der(K) $ by virtue of the invariance of $ K(n, m) $ under $ Der(\overline{K}) $.