LOW-DIMENSIONAL COHOMOLOGY OF LIE SUPERALGEBRA A(1,0) WITH COEFFICIENTS IN WITT OR SPECIAL SUPERALGEBRAS

Over a field of characteristic p > 2, using a direct sum decomposition of submodules and the weight space decomposition for the Witt superalgebra viewed as A(1, 0)-module, we compute the low-dimensional cohomology groups of the special linear Lie superalgebra A(1, 0) with coefficients in the Witt superalgebra. We also compute the low-dimensional cohomology groups of A(1, 0) with coefficients in the Special superalgebra.