Cohomology Of Lie Superalgebra Q(3) With Coefficients In Restricted Verma Modules

Suppose that the underlying field is of characteristic p>2.In this paper,firstly,the restricted Verma module of Lie superalgebra q(3)is constructed by the triangular decomposition of q(3)and the definition of induced modules.Then,the weight space decompositions of restricted Verma modules of three weights are carried out.Next,the weight derivations of q(3)to the restricted Verma modules of three weights are calculated.Finally,we get that the first cohomology of Lie superalgebra q(3)with coefficients in the restricted Verma modules of three weights is trivial.