W(2)到Kac模的0阶上同调

Zeroth cohomology from W(2)to Kac modules

确定了特征p≥3的域上Witt型模李超代数W(2)到所有限制以及非限制Kac模K S(λ)的0阶上同调.得出以下结论:当S=0,λ=(0,2)时,W(2)到限制Kac模K S(λ)的0阶上同调空间是一维的;否则,W(2)到Kac模K S(λ)的0阶上同调空间都是零维的.

Over a field of characteristic p≥3,this paper determines the 0-th cohomology from Witt-type Modular Lie superalgebra W(2)to all restricted and non-restricted Kac modules K S(λ).We show that the 0-th cohomology spaces of W(2)with coefficients in K S(λ)is 1-dimensional if S=0,λ=(0,2),and the 0-th cohomology spaces of W(2)with coefficients in K S(λ)is 0-dimensional if S≠0 orλ≠(0,2).