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Cohomological invariants for orthogonal involutions on degree 8 algebras

Published online by Cambridge University Press:  05 July 2011

Anne Quéguiner-Mathieu  and
Jean-Pierre Tignol
Anne Quéguiner-Mathieu
Affiliation:
LAGA - UMR 7539 du CNRS, Université Paris 13, F-93430 Villetaneuse and UPEC, F-94010 Créteil, Francequeguin@math.univ-paris13.fr
Jean-Pierre Tignol
Affiliation:
Zukunftskolleg, Universität Konstanz, D-78457 Konstanz, Germany and ICTEAM Institute, Université catholique de Louvain, B-1348 Louvain-la-Neuve, BelgiumJean-Pierre.Tignol@uclouvain.be
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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 non isomorphic involutions with trivial relative Arason invariant.

Keywords

Cohomological invariantorthogonal groupalgebra with involutionClifford algebrahalf-neighbortriality
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 2 , April 2012 , pp. 333 - 358
Copyright
Copyright © ISOPP 2011

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