Référence Bibliographique
"Cohomological invariants for orthogonal involutions on degree 8 algebras" Quéguiner-Mathieu, Anne ; Tignol, Jean-Pierre 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. Document type : Article de périodique (Journal article) Référence bibliographique Quéguiner-Mathieu, Anne ; Tignol, Jean-Pierre. Cohomological invariants for orthogonal involutions on degree 8 algebras. In: Journal of K-Theory : k-theory and its applications to algebra, geometry, analysis and topology, Vol. 9, no. 2, p. 333-358 (2012) DOI : 10.1017/is011006015jkt160 Available at: http://hdl.handle.net/2078.1/110505 [Downloaded 2019/05/08 at 12:52:58 ] J. K-Theory 9 (2012), 333–358 ©2011 ISOPP doi:10.1017/is011006015jkt160 Cohomological invariants for orthogonal involutions on degree 8 algebras by ANNE QUÉGUINER-MATHIEU AND JEAN-PIERRE TIGNOL 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. Key Words: Cohomological invariant, orthogonal group, algebra with involu- tion, Clifford algebra, half-neighbor, triality Mathematics Subject Classification 2010: 11E72, 11E81, 16W10 1. Introduction 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 classifies quadratic forms of dimension 2, while the even part of the Clifford algebra classifies forms of dimension 4.
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