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


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.


Quadratic Form Tensor Product Clifford Algebra Algebra Homomorphism Quaternion Algebra 
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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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