The Lie algebra of derivations of a current Lie algebra

Let K be a field of characteristic zero, g be a finite dimensional K-Lie algebra and let A be a finite dimensional associative and commutative K-algebra with unit. We describe the structure of the Lie algebra of derivations of the current Lie algebra g_A = g ⊗_K A, denoted by Der(g_A). Furthermore, we obtain the Levi decomposition of Der(g_A). As a consequence of the last result, if h_m is the Heisenberg Lie algebra of dimension 2m + 1, we obtain a faithful representation of Der(h_m,k) of the current truncated Heisenberg Lie algebra h_m,k = h_m ⊗ K[t]/(t^k+1) for all positive integer k.