The second cohomology of sl(m|1) with coefficients in its enveloping   algebra is trivial
  Using techniques developed in a recent article by the authors, it is proved that the 2-cohomology of the Lie superalgebra sl(m|1); m > 1, with coefficients in its enveloping algebra is trivial. The obstacles in solving the analogous problem for sl(3|2) are also discussed. 
M. Scheunert and R. B. Zhang