A classification of the division algebras that are isotopic to a cyclic Galois field extension

2024/07/16 by Pumpluen, Susanne
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2407.11598

Abstract

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree n>2 up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The classification is ``tight'' in the sense that the list of algebras has features that make it easy to distinguish non-isomorphic ones.

Related

• The cyclicity problem for Albert algebras
• The isotopy classes of Petit division algebras
• Division algebras, Galois fields, quadratic residues
• Semifields from skew polynomial rings
• A condition for cyclic algebras to be split