2024/03/23 by Susanne Pumpluen, Pumpluen, Susanne · 1 citation
Mathematics · #17A35 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2403.15914
openalex publication_date 2024/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.