2024/06/17 by Monica Nevins, Nevins, Monica, Susanne Pumpluen +1 · 2 citations
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2406.11419
openalex publication_date 2024/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine and explicitly parametrize the isomorphism classes of nonassociative quaternion algebras over a field of characteristic different from two, as well as the isomorphism classes of nonassociative cyclic algebras of odd prime degree when the base field contains a primitive mth root of unity. In the course of doing so, we prove that any two such algebras can be isomorphic only if the cyclic field extension and the chosen generator of the Galois group are the same. As an application, we give a parametrization of nonassociative cyclic algebras of prime degree over a local nonarchimedean field F, which is entirely explicit under mild hypotheses on the residual characteristic. In particular, this gives a rich understanding of the important class of nonassociative quaternion algebras up to isomorphism over nonarchimedean local fields.