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.

18 pages

References in corpus (3)

• Finite nonassociative algebras obtained from skew polynomials and possible applications to $(f,\sigma ,\delta )$-codes
• Nonassociative cyclic extensions of fields and central simple algebras
• Petit Algebras and their Automorphisms