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Archiv der Mathematik

, Volume 93, Issue 2, pp 129–138 | Cite as

Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4

  • Alexandre Masquelein
  • Anne Quéguiner-Mathieu
  • Jean-Pierre Tignol
Article

Abstract

Izhboldin and Karpenko proved in Math. Z. (234 (2000), 647–695, Theorem 16.10) that any quadratic form of dimension 8 with trivial discriminant and Clifford algebra of index 4 is isometric to the transfer, with respect to some quadratic étale extension, of a quadratic form similar to a two-fold Pfister form. We give a new proof of this result, based on a theorem of decomposability for degree 8 and index 4 algebras with orthogonal involution.

Keywords

Quadratic Form Tensor Product Clifford Algebra Algebra Homomorphism Quaternion Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Alexandre Masquelein
    • 1
  • Anne Quéguiner-Mathieu
    • 2
  • Jean-Pierre Tignol
    • 1
  1. 1.Département de MathématiquesUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Université Paris 13 (LAGA), CNRS (UMR 7539), Université Paris 12 (IUFM)VilletaneuseFrance

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