Cohomological invariants for G-Galois algebras and self-dual normal bases

TL;DR

This paper introduces degree two cohomological invariants for G-Galois algebras over fields of characteristic not 2, providing necessary and sometimes sufficient conditions for the existence of self-dual normal bases.

Contribution

It defines new cohomological invariants and applies them to characterize when self-dual normal bases exist in G-Galois algebras.

Findings

Cohomological invariants give necessary conditions for self-dual normal bases.

In some cases, these conditions are also sufficient.

The invariants help classify G-Galois algebras with self-dual bases.

Abstract

We define degree two cohomological invariants for G-Galois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self--dual normal basis. In some cases, we show that these conditions are also sufficient.