The automorphisms of differential extensions of characteristic \(p\)

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 \(F\)...

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Bibliographic Details
Published inarXiv.org
Main Author Pumpluen, Susanne
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 13.06.2024
Subjects
Algebra
Automorphisms
Polynomials
Rings (mathematics)
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Summary: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.
ISSN:2331-8422