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Pfister involutions

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Abstract

The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to a Pfister form. Moreover, cohomological invariants of those algebras with involution are discussed.

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Authors and Affiliations

  1. Département de Mathématiques, Ecole Polytechnique, Fédérale de Lausanne, 1015, Lausanne, Switzerland

    E Bayer-Fluckiger

  2. Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Mumbai, India

    R Parimala

  3. UMR 7539 du CNRS, Département de Mathématiques, Université Paris, 13, F-93430, Villetaneuse, France

    A Quéguiner-Mathieu

Authors
  1. E Bayer-Fluckiger
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  2. R Parimala
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  3. A Quéguiner-Mathieu
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Correspondence to E Bayer-Fluckiger.

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Bayer-Fluckiger, E., Parimala, R. & Quéguiner-Mathieu, A. Pfister involutions. Proc. Indian Acad. Sci. (Math. Sci.) 113, 365–377 (2003). https://doi.org/10.1007/BF02829631

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  • DOI: https://doi.org/10.1007/BF02829631

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