On the homology of Lie algebras like $\mathfrak{g}\mathfrak{l}(\mathrm{\infty },R)$

We revisit a recent paper of Fialowski and Iohara. They compute the homology of the Lie algebra $\mathfrak{g}\mathfrak{l}(\mathrm{\infty },R)$ for $R$ an associative unital algebra over a field of characteristic zero. We explain how to obtain essentially the same results by a completely different method.