A. Quéguiner-Mathieu and J.-P. Tignol: Cohomological invariants for orthogonal involutions on degree 8 algebras


Submission: 2010, Dec 17

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 pro- duce explicit examples, in index 4 and 8, of non isomorphic involutions with trivial relative Arason invariant.

2010 Mathematics Subject Classification: 16W10 ; 11E04

Keywords and Phrases: Cohomological invariant ; Orthogonal involution ; Half-neighbor ; Triality

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