The automorphisms of generalized cyclic Azumaya algebras

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.