Cohomological invariants for orthogonal involutions on degree 8 algebras

Abstract

Using triality, we define a relative Arason invariant for orthogonal involutions on a -possibly division- central simple algebra of degree 8. This invariant detects hyperbolicity, but it does not detect isomorphism. We produce explicit examples, in index 4 and 8, of nonisomorphic involutions with trivial relative Arason invariant.