Central extensions of Steinberg Lie superalgebras of small rank
  It was shown by A.V.Mikhalev and I.A.Pinchuk in [MP] that the second homology group $H_2(\st)$ of the Steinberg Lie superalgebra $\st$ is trivial for $m+n\geq 5$. In this paper, we will work out $H_2(\st)$ explicitly for $m+n=3, 4$. 
Hongjia Chen, Yun Gao, Shikui Shang