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

Over a field of characteristic [Formula: see text], the first cohomology of the orthogonal symplectic Lie superalgebra [Formula: see text] 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 [Formula: see text]. As a byproduct, the first cohomology of [Formula: see text] with coefficients in the restricted enveloping algebra (under the adjoint action) is not trivial.