2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159907Let $A$ be a unital commutative associative algebra over a field of characteristic zero, $\k$ be a Lie algebra, and $\z$ a vector space, considered as a trivial module of the Lie algebra $\g := A \otimes \k$. In this paper we give a description of the cohomology space $H^2(\g,\z)$ in terms of well accessible data associated to $A$ and $\k$. We also discuss the topological situation, where $A$ and $\k$ are locally convex algebras.Some minor corrections have been made in this versionRings and Algebras17B56; 17B65text