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Composition Algebras and Outer Automorphisms of Algebraic Groups (1504.01278v1)
Published 6 Apr 2015 in math.RA and math.GR
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.