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The automorphisms of generalized cyclic Azumaya algebras

Pumpluen, S

The automorphisms of generalized cyclic Azumaya algebras Thumbnail


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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.

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

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