The automorphisms of differential extensions of characteristic p

Pumplün, S.

Abstract

Nonassociative differential extensions are generalizations of associative differential extensions, either of a purely inseparable field extension K of exponent one of a field F, F of characteristic p, or of a central division algebra over a purely inseparable field extension of F. Associative differential extensions are well known central simple algebras first defined by Amitsur and Jacobson. We explicitly compute the automorphisms of nonassociative differential extensions. These are canonically obtained by restricting automorphisms of the differential polynomial ring used in the construction of the algebra. In particular, we obtain descriptions for the automorphisms of associative differential extensions of D and K, which are known to be inner.

Citation

Pumplün, S. (2024). The automorphisms of differential extensions of characteristic p. Results in Mathematics, 79(5), Article 196. https://doi.org/10.1007/s00025-024-02234-z

• Journal Article Type: Article
• Acceptance Date: Jun 20, 2024
• Online Publication Date: Jul 9, 2024
• Publication Date: 2024-08
• Deposit Date: Jun 20, 2024
• Publicly Available Date: Jul 10, 2025
• Journal: Results in Mathematics
• Print ISSN: 1422-6383
• Electronic ISSN: 1420-9012
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 79
• Issue: 5
• Article Number: 196
• DOI: https://doi.org/10.1007/s00025-024-02234-z
• Keywords: differential polynomial, nonassociative division algebra, Secondary 17A60, Differential polynomial ring, skew polynomial, 17A36, 16S32, Primary 17A35, automorphisms, differential extension
• Public URL: https://nottingham-repository.worktribe.com/output/36301254
• Additional Information: Received: 25 March 2024; Accepted: 20 June 2024; First Online: 9 July 2024; : ; : The author has no relevant financial or non-financial interests to disclose.; : Ethics approval and consent to participate Not applicable.; : Not applicable.