On cubic etale algebras

We describe explicitly a group structure on isomorphism classes of cubic etale algebras with prescribed discriminant. The case of trivial discriminant corresponds to the group of cubic cyclic algebras.6728129

Totally decomposable symplectic and unitary involutions

We study totally decomposable symplectic and unitary involutions on central simple algebras of index 2 and on split central simple algebras respectively. We show that for every field extension, these involutions are either anisotropic or hyperbolic after extending scalars, and that the converse holds if the algebras are of 2-power degree. These results are new in characteristic 2, otherwise were shown in [3] and [6] respectively.Comment: 11 page