Composition algebras and outer automorphisms of algebraic groups via triality |
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Authors: | Seidon Alsaody |
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Institution: | 1. Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, Francealsaody@math.univ-lyon1.fr |
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Abstract: | In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form n over a field k of characteristic not two, and a category arising from an action of the projective similarity group of n on certain pairs of automorphisms of the group scheme PGO+(n) defined over k. This extends results recently obtained in the same direction for symmetric composition algebras. We also derive known results on composition algebras from our equivalence. |
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Keywords: | Affine group schemes composition algebras outer automorphisms triality |
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