The automorphisms of generalized cyclic Azumaya algebras

Pumpluen, S

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.

Citation

Pumpluen, S. (2021). The automorphisms of generalized cyclic Azumaya algebras. Journal of Pure and Applied Algebra, 225(4), Article 106540. https://doi.org/10.1016/j.jpaa.2020.106540

• Journal Article Type: Article
• Acceptance Date: Jul 9, 2020
• Online Publication Date: Aug 24, 2020
• Publication Date: Apr 1, 2021
• Deposit Date: Aug 26, 2020
• Publicly Available Date: Aug 25, 2021
• Journal: Journal of Pure and Applied Algebra
• Print ISSN: 0022-4049
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 225
• Issue: 4
• Article Number: 106540
• DOI: https://doi.org/10.1016/j.jpaa.2020.106540
• Keywords: Rings and Algebras
• Public URL: https://nottingham-repository.worktribe.com/output/2461413
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0022404920302413