On Solvability of Automorphism Groups of Commutative Algebras

Let $A$ be a finite-dimensional commutative associative algebra with unity over an algebraically closed field $\mathbb{K}$. The purpose of the paper is to study the solvability of $G_A$, where $G_A$ is the identity component of ${\text{Aut}}_{\mathbb{K}}(A)$. Inspired by Pollack’s work, Saorín and Asensio have started this study for a commutative associative algebra $A$ when $\text{dim}(R\mathrm{/}{R}^2)=2$, where $R$ is the Jacobson radical of $A$. In this paper, we give new sufficient conditions on $A$ so that $G_A$ is solvable without any restriction on $\text{dim}(R\mathrm{/}{R}^2)$.