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Let 
$A$ be a unital commutative associative algebra over a field of characteristic zero, 
$\mathfrak{k}$ a Lie algebra, and 
$\mathfrak{z}$ a vector space, considered as a trivial module of the Lie algebra 
$\mathfrak{g}:=A\otimes \mathfrak{k}$. In this paper, we give a description of the cohomology space 
${{H}^{2}}(\mathfrak{g},\mathfrak{z})$ in terms of easily accessible data associated with $A$ and $\mathfrak{k}$. We also discuss the topological situation, where $A$ and $\mathfrak{k}$ are locally convex algebras.
