李超代数P(2)到限制Verma模的一维上同调  

One-dimensional cohomology of Lie superalgebra P(2)with coefficients in restricted Verma modules

作　　者：霍雪童 孙丽萍 王淑娟 HUO Xue-tong;SUN Li-ping;WANG Shu-juan(School of Science,Harbin University of Science and Technology,Harbin 150080,China;Liberal Arts College,Shanghai Maritime University,Shanghai 200135,China)

机构地区：[1]哈尔滨理工大学理学院,黑龙江哈尔滨150080 [2]上海海事大学文理学院,上海200135

出　　处：《东北师大学报（自然科学版）》2023年第3期1-5,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11701158);黑龙江省自然科学基金资助项目(A2015017,QC2018006).

摘　　要：在特征p>3的域上,利用P(2)的三角分解以及诱导模的定义,构造出P(2)的限制Verma模,并对不同权的限制Verma模进行了权空间分解.计算了P(2)到这几个权空间的权导子,进而得到P(2)到限制Verma模的一维上同调是平凡的.Over a field of characteristic p>3,the restricted Verma modules of P(2)are constructed by using the triangular decomposition and the definition of induced modules,and the restricted Verma modules with different weights are decomposed in weight space.The weight derivations of P(2)with these weight spaces are calculated,and it is obtained that the one-dimensional cohomology of P(2)with restricted Verma modules is trivial.

关 键 词：分解 VERMA模 权导子 上同调 

分 类 号：O152.5[理学—数学]