Local superderivations of Lie superalgebra $ \mathrm{osp}(1, 2) $ to all simple modules-Reference-Cited by-同舟云学术

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

Published:2024 Issue:8 Volume:9 Page:22655-22664
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zhao Shiqi¹,Liu Wende¹,Wang Shujuan²

Affiliation:

1. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

2. School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China

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>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference14 articles.

1. S. Ayupov, K. Kudaybergenov, Local derivations on finite-dimensional Lie algebras, Linear Algebra Appl., 493 (2016), 381–398. https://doi.org/10.1016/j.laa.2015.11.034

2. S. A. Ayupov, A. K. Kudaybergenov, Local derivations on solvable Lie algebras, Linear Multilinear Algebra, 69 (2021), 1286–1301. https://doi.org/10.1080/03081087.2019.1626336

3. L. M. Camacho, R. M. Navarro, B. Omirov, Local superderivations on solvable Lie and Leibniz superalgebras, Mediterr. J. Math., 20 (2023), 76. https://doi.org/10.1007/s00009-023-02284-7

4. H. X. Chen, Y. Wang, Local superderivations on Lie superalgebras q(n), Czechoslov. Math. J., 68 (2018), 661–675. https://doi.org/10.21136/CMJ.2018.0597-16

5. H. X. Chen, Y. Wang, J. Z. Nan, Local superderivations on basic classical Lie superalgebras, Algebra Colloq., 24 (2017), 673–684. https://doi.org/10.1142/S100538671700044X