Cohomological invariants for orthogonal involutions on degree 8 algebras

Quéguiner-Mathieu, Anne;Tignol, Jean-Pierre
(2012) Journal of K-Theory : k-theory and its applications to algebra, geometry, analysis and topology — Vol. 9, n° 2, p. 333-358 (2012)

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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.
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Quéguiner-Mathieu, A., & Tignol, J.-P. (2012). Cohomological invariants for orthogonal involutions on degree 8 algebras. Journal of K-Theory : k-theory and its applications to algebra, geometry, analysis and topology, 9(2), 333-358. https://doi.org/10.1017/is011006015jkt160 (Original work published 2012)