摘要
设α是域F上的结合超代数满足[α,α]=α或α=F．证明了当m+n>1时,H2(glm|n(α),F)(?)HC1(α,F)．定义了一大类广义微分算子李超代数,作为W-无穷代数W∞(glN)的推广．确定了这些李超代数的2-上循环．同时给出了矩阵量子微分算子李超代数的2-上同调群．
For any unital associative superalgebra a over a field F satisfying [α, α] = α or α = F, the authors prove H^2（gιm｜n（α）,F） ≌ HC^1（α,F）. As an application, by defining a large class of Lie superalgebras of generalized matrix differential operators which are generalizations of the W-infinity algebras W∞（gιN）, the authors determine the 2-cocycles of these Lie superalgebras. The result can also be applied to obtain the 2-cohomology groups of Lie superalgebras of matrix quantum differential operators.
出处
《数学年刊（A辑）》
CSCD
北大核心
2006年第4期527-534,共8页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10471091)
中国科技大学"百人计划"和教育部跨世纪优秀人才培养计划资助的项目
