Skip to main content
SpringerLink
Log in

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

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arason J.K.: Cohomologische Invarianten quadratischer Formen. J. Alg. 36, 448–491 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Becher K.J.: A proof of the Pfister factor conjecture. Invent. Math. 173, 1–6 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dejaiffe I.: Somme orthogonale d’algèbres à involution et algèbre de Clifford. Comm. Algebra 26(5), 1589–1612 (1995)

    Article  MathSciNet  Google Scholar 

  4. Hoffmann D.W., Tignol J.-P.: On 14-dimensional quadratic forms in I 3, 8-dimensional forms in I 2, and the common value property. Doc. Math. 3, 189–214 (1998) (electronic)

    MATH  MathSciNet  Google Scholar 

  5. Izhboldin O.T., Karpenko N.A.: Some new examples in the theory of quadratic forms. Math. Z. 234, 647–695 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. M.-A. Knus et al., The book of involutions, Colloquium Publ., 44, Amer. Math. Soc., Providence, RI, 1998.

  7. Knebusch M.: Generic splitting of quadratic forms. II. Proc. London Math. Soc. 34(3), 1–31 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  8. T.-Y. Lam, Introduction to quadratic forms over fields, Grad. Studies in Math., 67, Amer. Math. Soc., 2005.

  9. Lewis D.W., Tignol J.-P.: Classification theorems for central simple algebras with involution. Manuscripta Math. 100, 259–276 (1999) With an appendix by R. Parimala

    Article  MATH  MathSciNet  Google Scholar 

  10. Sivatski A.S.: Applications of Clifford algebras to involutions and quadratic forms. Comm. Algebra 33, 937–951 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Tao D.: The generalized even Clifford algebra. J. Algebra 172, 184–204 (1995)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Université catholique de Louvain, Chemin du cyclotron, 2, 1348, Louvain-la-Neuve, Belgium

    Alexandre Masquelein & Jean-Pierre Tignol

  2. Université Paris 13 (LAGA), CNRS (UMR 7539), Université Paris 12 (IUFM), 93430, Villetaneuse, France

    Anne Quéguiner-Mathieu

Authors
  1. Alexandre Masquelein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anne Quéguiner-Mathieu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean-Pierre Tignol
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anne Quéguiner-Mathieu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Masquelein, A., Quéguiner-Mathieu, A. & Tignol, JP. Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4. Arch. Math. 93, 129–138 (2009). https://doi.org/10.1007/s00013-009-0019-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-009-0019-2

Keywords

Search

Navigation