2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106141It is well-known that the second homology group $H_2(\st)$ of the Steinberg Lie algebra $\st$ is trivial when $n\geq 5$. In this paper, we will work out $H_2(\st)$ explicitly for $n=3, 4$ which are not necessarily trivial. Consequently, we obtained $H_2(sl_n(R))$ for $n=3, 4$.22 pagesQuantum AlgebraK-Theory and Homology17B55, 17B60text