# The automorphisms of generalized cyclic Azumaya algebras

## TL;DR

This paper introduces a nonassociative generalization of cyclic Azumaya algebras using skew polynomial rings and characterizes their automorphisms, including inner automorphisms, extending classical results.

## Contribution

It defines a new class of nonassociative algebras based on skew polynomial rings and describes their automorphism groups, generalizing known results for classical Azumaya and central simple algebras.

## Key findings

- Automorphisms are induced by ring automorphisms of skew polynomial rings.
- Inner automorphisms are explicitly characterized.
- Classical Azumaya algebra automorphisms are special cases.

## Abstract

We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings $D[t;\sigma]$, where $D$ is an Azumaya algebra of constant rank with center $C$ and $\sigma$ an automorphism of $D$, such that $\sigma|_{C}$ has finite order. The automorphisms of these algebras are canonically induced by ring automorphisms of the skew polynomial ring $D[t;\sigma]$ used in their construction. We achieve a description of their inner automorphisms. Results on the automorphisms of classical Azumaya algebras and central simple algebras of this type are obtained as special cases.