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The canonical quadratic pair on a Clifford algebra and triality

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Abstract

We define a canonical quadratic pair on the Clifford algebra of an algebra with quadratic pair over a field. This allows us to extend to the characteristic 2 case the notion of trialitarian triples, from which we derive a characterization of totally decomposable quadratic pairs in degree 8. We also describe trialitarian triples involving algebras of small Schur index.

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Acknowledgments

We are grateful to Seidon Alsaody, Philippe Gille and Jean-Pierre Tignol for insightful discussions

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Authors and Affiliations

  1. Departement Wiskunde-Informatica, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Andrew Dolphin

  2. Laboratoire Analyse, Géométrie et Applications, Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse, France

    Anne Quéguiner-Mathieu

Authors
  1. Andrew Dolphin
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  2. Anne Quéguiner-Mathieu
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Correspondence to Anne Quéguiner-Mathieu.

Additional information

Both authors gratefully acknowledge the support of the French ministries MEAE and MESRI and of the FWO, under the rubric of the Tournesol fund #VS05018N.

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Dolphin, A., Quéguiner-Mathieu, A. The canonical quadratic pair on a Clifford algebra and triality. Isr. J. Math. 242, 171–213 (2021). https://doi.org/10.1007/s11856-021-2128-y

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  • DOI: https://doi.org/10.1007/s11856-021-2128-y

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