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

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 istight'' in the sense that the list of algebras has features that make it easy to distinguish non-isomorphic ones.