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arXiv · 1504.01278

Composition Algebras and Outer Automorphisms of Algebraic Groups

Seidon Alsaody
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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 $\mathbf{PGO}^+(n)$ 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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Seidon Alsaody. 2015-04-06. Composition Algebras and Outer Automorphisms of Algebraic Groups. https://doi.org/10.1080/00927872.2016.1175603

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