%0 Journal Article %T Second homology groups and universal coverings of Steinberg Leibniz algebras of small characteristic %A Qifen Jiang %A Ran Shen %A Yucai Su %J Mathematics %D 2006 %I arXiv %X It is known that the second Leibniz homology group $HL_2(stl_n(R))$ of the Steinberg Leibniz algebra $stl_n(R)$ is trivial for $n\geq 5$. In this paper, we determine $HL_2(stl_n(R))$ explicitly (which are shown to be not necessarily trivial) for $n=3, 4$ without any assumption on the base ring. %U http://arxiv.org/abs/math/0608406v2