Finite presentability of universal central extensions of ${\mathfrak{s}\mathfrak{l}}_n$

In this paper we discuss finite presentability of the universal central extensions of Lie algebras ${\mathfrak{s}\mathfrak{l}}_n(R)$, where $n\ge 3$ and $R$ is a unital associative $k$-algebra. We show that a universal central extension is finitely presented if and only if the algebra $R$ is finitely presented.