A solvability criterion for the Lie algebra of derivations of a fat point (Q975096)

\textit{J. N. Mather} and \textit{S. S.-T. Yau} proved [Invent. Math. 69, 243--251 (1982; Zbl 0499.32008)] that the Lie algebra of derivations \(L(X)\) of the Tyurina algebra \(A(X)\) associated to an isolated hypersurface singularity \(X \subset (\mathbb{C}^n, 0)\) is solvable. The paper under review is devoted to extend this result to the case of a Lie algebra of derivations of a zero-dimensional local complex algebra, by asserting that if \(S\) is a zero-dimensional local \(\mathbb{C}\)-algebra of embedding dimension \(\text{embdim}(S)\) and order \(\text{ord}(S)\), and it is denoted by \(\varepsilon_1(S)\) its first derivation. Then the Lie algebra \(\text{Der}_{\mathbb{C}}S\) is solvable if \(\varepsilon_1(S)+1 < \text{embdim}(S) + \text{ord}(S)\).