两类Heisenberg李超代数的标准上同调  

Standard Cohomology of Two Types of Heisenberg Lie Superalgebra

作　　者：江薇 远继霞[1] JIANG Wei;YUAN Jixia(School of Mathematical Science,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《吉林大学学报（理学版）》2023年第5期1051-1055,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12271085);黑龙江省自然科学基金(批准号:LH2022A019);黑龙江省省属高等学校基本科研业务费项目(批准号:2020-KYYWF-1018);黑龙江大学杰出青年科学基金(批准号:JCL202103).

摘　　要：利用微分复形计算4维偶中心与3维奇中心Heisenberg李超代数系数取自于1维平凡模的标准上同调.首先,计算这两类Heisenberg李超代数的微分算子;其次,计算这两类Heisenberg李超代数系数取自于1维平凡模的标准上同调.并给出这两类代数标准上同调的基底和维数.We used the differential complex to calculate the standard cohomology of 4-dimensional even centers and 3-dimensional odd centers Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules.Firstly,we calculated the differential operators of these two classes of Heisenberg Lie superalgebras.Secondly,we calculated the standard cohomology of these two types of Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules.In particular,we obtained the basis and dimension of the standard cohomology for these two types of Heisenberg Lie superalgebras.

关 键 词：李超代数 Heisenberg李超代数 标准上同调 

分 类 号：O154.2[理学—数学]