Low-dimensional cohomology of Lie superalgebra slm|nslm|n with coefficients in Witt or Special superalgebras

Over a field of characteristic p>2p>2, the Witt superalgebras are viewed as modules of the special linear Lie superalgebra slm|nslm|n by means of the adjoint representation. The low-dimensional cohomology groups of slm|nslm|n with coefficients in Witt superalgebras are computed by virtue of the direct sum decomposition of submodules and the weight space decompositions of these submodules relative to the standard Cartan subalgebra of slm|nslm|n. Then we are able to obtain the low-dimensional cohomology groups of slm|nslm|n with coefficients in Special superalgebras, which are slm|nslm|n-submodules of Witt superalgebras.