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.
Citation: Shiqi Zhao, Wende Liu, Shujuan Wang. Local superderivations of Lie superalgebra $ \mathrm{osp}(1, 2) $ to all simple modules[J]. AIMS Mathematics, 2024, 9(8): 22655-22664. doi: 10.3934/math.20241103
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.
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Shiqi Zhao, Wende Liu, Shujuan Wang. Local superderivations of Lie superalgebra $ \mathrm{osp}(1, 2) $ to all simple modules[J]. AIMS Mathematics, 2024, 9(8): 22655-22664. doi: 10.3934/math.20241103
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