The matrix representation of the first cohomology of $\frak{gl}_{0|2}$ with coefficients in the generalized Witt Lie superalgebra

Abstract: This paper is primarily concerned with the first cohomology of $\frak{gl}{0|2}$ with coefficients in the generalized Witt Lie superalgebra, where $\frak{gl}{0|2}$ is a subalgebra of the general linear Lie superalgebra. The derivations and inner derivations from $\frak{gl}{0|2}$ into submodules of the generalized Witt Lie superalgebra are represented by matrices, respectively. Then the first cohomology of $\frak{gl}{0|2}$ with coefficients in the generalized Witt Lie superalgebra is completely determined by matrices.