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

TL;DR

This paper establishes a solvability criterion for the Lie algebra of derivations of a zero-dimensional local complex algebra, generalizing known results for hypersurface singularities.

Contribution

It introduces an inequality involving embedding dimension, order, and first deviation that guarantees solvability of the Lie algebra, extending previous work on Yau algebras.

Findings

Derived a new inequality ensuring Lie algebra solvability

Generalized solvability conditions from hypersurface singularities

Provided a criterion applicable to zero-dimensional local algebras

Abstract

We consider the Lie algebra of derivations of a zero dimensional local complex algebra. We describe an inequality involving the embedding dimension, the order, and the first deviation that forces this Lie algebra to be solvable. Our result was motivated by and generalizes the solvability of the Yau algebra of an isolated hypersurface singularity.