On Christophersen's problem

Abstract

Let $A$ be a finite-dimensional (Artinian) Gorenstein algebra, and let $\operatorname{Aut}(A)^{\circ}$ denote the connected component of the identity in the automorphism group of $A$. We introduce a new subclass of Gorenstein algebras and prove that for any algebra $A$ in this subclass, the group $\operatorname{Aut}(A)^{\circ}$ is solvable. This result is closely related to the Christophersen problem in the theory of local algebras.