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

作　　者：Shujuan Wang Wende Liu 

机构地区：[1]School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China [2]School of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China

出　　处：《Algebra Colloquium》2023年第4期599-614,共16页代数集刊（英文版）

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

摘　　要：Over a field of characteristic p>0,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.

关 键 词：orthogonal symplectic Lie superalgebras baby Verma modules simple modules COHOMOLOGY 

分 类 号：O153.3[理学—数学]