The discriminant controls automorphism groups of noncommutative algebras

TL;DR

This paper employs the discriminant to analyze and determine the automorphism groups of certain noncommutative algebras, demonstrating that some families have manageable automorphism structures.

Contribution

It introduces a discriminant-based method to explicitly compute automorphism groups of noncommutative algebras, advancing understanding in noncommutative algebra theory.

Findings

Discriminant effectively determines automorphism groups.

Certain noncommutative algebra families have tractable automorphism groups.

Method simplifies automorphism group analysis.

Abstract

We use the discriminant to determine the automorphism groups of some noncommutative algebras, and we prove that a family of noncommutative algebras has tractable automorphism groups.