2011
DOI: 10.1017/is011006015jkt160
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Cohomological invariants for orthogonal involutions on degree 8 algebras

Abstract: 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 non isomorphic involutions with trivial relative Arason invariant.The discriminant and the Clifford algebra are classical invariants of quadratic forms over a field F of characteristic different from 2. Up to similarity, the discriminant c… Show more

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Cited by 7 publications
(9 citation statements)
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“…Because (M 4 (Q), σ 0 ) has trivial discriminant and Clifford invariant, by [35,Th. 5.2] we may find λ, µ ∈ F × and an orthogonal involution ρ on Q such that…”
Section: Consider Three Quaternion Division Algebrasmentioning
confidence: 96%
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“…Because (M 4 (Q), σ 0 ) has trivial discriminant and Clifford invariant, by [35,Th. 5.2] we may find λ, µ ∈ F × and an orthogonal involution ρ on Q such that…”
Section: Consider Three Quaternion Division Algebrasmentioning
confidence: 96%
“…Hence, the formula given in [35,Th. 5.5] for algebras of degree 8 is actually valid in arbitrary degree.…”
Section: By the Additivity Property (1) The Connecting Mapmentioning
confidence: 99%
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