Local superderivations of Lie superalgebra $ \mathrm{osp}(1, 2) $ to all simple modules

Abstract

<p>In this paper, we consider the orthogonal symplectic Lie superalgebra $ \mathrm{osp}(1, 2) $ over an algebraically closed field of prime characteristic $ p > 2 $. Using the classification of the simple modules of the Lie superalgebra $ \mathrm{osp}(1, 2) $, we prove that every local superderivation of $ \mathrm{osp}(1, 2) $ to any simple module is a superderivation.</p>