On Christophersen's problem

TL;DR

This paper introduces a new subclass of Artinian Gorenstein algebras and proves that their automorphism groups are solvable, addressing a problem in the theory of local algebras related to Christophersen's problem.

Contribution

The paper defines a novel subclass of Gorenstein algebras and establishes the solvability of their automorphism groups, advancing understanding of their symmetry properties.

Findings

Automorphism groups of the new subclass are solvable.

The result provides insights into the structure of local Gorenstein algebras.

Addresses the Christophersen problem in algebra theory.

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.