On the classification of rational four-dimensional unital division algebras
Gustav Hammarhjelm

TL;DR
This paper advances the classification of four-dimensional unital division algebras over the rationals, focusing on non-associative structures with specific automorphism groups and subfield properties.
Contribution
It specializes prior general results to the rational case, providing explicit families and classification methods for certain non-associative division algebras and Galois extensions.
Findings
Explicit two-parameter families of non-isomorphic non-associative algebras with subfield $\, ext{l}$
Classification methods for central skew fields with given subfields
Complete classification of Galois extensions with Galois group V containing specific subfields
Abstract
In a paper by E. Dieterich 2017, the category of four-dimensional unital division algebras, whose right nucleus is non-trivial and whose automorphism group contains Klein's four group , is studied over a general ground field with . In particular, the objects in are exhaustively constructed from parameters in and explicit isomorphism conditions for the constructed objects are found in terms of these parameters. In this paper, we specialize to the case and present results towards a classification of . In particular, for each field with we present explicity a two-parameter family of pairwise non-isomorphic non-associative objects in that admit as a subfield and we provide a method for classifying the full subcategory of…
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