Universal coverings of Steinberg Lie algebras of small characteristic

It is well known that the second homology group H2(stn(R)) of the Steinberg Lie algebra stn(R) is trivial when n⩾5. In this paper, we will work out H2(stn(R)) explicitly for n=3,4 which are not necessarily trivial. Consequently, we obtained H2(sln(R)) for n=3,4.