The First Cohomology of osp(1,2)with Coefficients in Baby Verma Modules and Simple Modules

作     者：Shujuan Wang Wende Liu Shujuan Wang;Wende Liu

作者机构：School of Mathematical SciencesHeilongjiang UniversityHarbin 150080China School of Mathematics and StatisticsHainan Normal UniversityHaikou 571158China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2023年第30卷第4期

页      面：599-614页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work is supported by Heilongjiang Provincial Natural Science Foundation of China(YQ2020A005) Natural Science Foundation of China(12061029) 

主　　题：orthogonal symplectic Lie superalgebras baby Verma modules simple modules cohomology 

摘      要：Over a field of characteristic p0,the first cohomology of the orthogonal symplectic Lie superalgebra osp(1,2)with coefficients in baby Verma modules and simple modules is determined by use of the weight space decompositions of these modules relative to a Cartan subalgebra of osp(1,2).As a byproduct,the first cohomology of osp(1,2)with coefficients in the restricted enveloping algebra(under the adjoint action)is not trivial.