Universal coverings of Steinberg Lie algebras of small characteristic

Abstract

It is well-known that the second homology group $H_2(\st)$ of the Steinberg Lie algebra $\st$ is trivial when $n\ge 5$. In this paper, we will work out $H_2(\st)$ explicitly for $n=3,4$ which are not necessarily trivial. Consequently, we obtained $H_2(s{l}_n(R))$ for $n=3,4$.

22 pages