The First Cohomology of osp(1,2)with Coefficients in Baby Verma Modules and Simple Modules

Over a field of characteristic p>0 , the first cohomology of the orthogonal symplectic Lie superalgebra o s p ( 1,2 ) with coefficients in baby Verma modules and simple modules is determined by use of the weight space decompositions of these modules relative to a Cartan subalgebra of o s p ( 1,2 ) . As a byproduct, the first cohomology of o s p ( 1,2 ) with coefficients in the restricted enveloping algebra (under the adjoint action) is not trivial.