A Note on Restricted Representations of the Witt Superalgebras  

作　　者：Yufeng YAO Bin SHU 

机构地区：[1]Department of Mathematics,Shanghai Maritime University [2]Department of Mathematics,East China Normal University

出　　处：《Chinese Annals of Mathematics,Series B》2013年第6期921-926,共6页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11126062,11201293,11226327,11271130);the Innovation Program of Shanghai Municipal Education Commission(Nos.12ZZ038,13YZ077)

摘　　要：Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.

关 键 词：Restricted Lie superalgebra Witt superalgebra Restricted representation Atypical weight 

分 类 号：O152.5[理学—数学]