Composition Algebras and Outer Automorphisms of Algebraic Groups
(English)Article in journal (Other academic) Submitted
In this note, we establish an equivalence of categories between the category of all eight-dimensionalcomposition algebras with any given quadratic form over a field of characteristic not two, and a category arising from anaction of the projective similarity group of on certain pairs of automorphisms of the group scheme defined ove . This extends results recently obtained in the same direction for symmetric composition algebras. We also derive known resultson composition algebras from our equivalence.
Composition algebras, algebraic groups, outer automorphisms, triality
IdentifiersURN: urn:nbn:se:uu:diva-248499OAI: oai:DiVA.org:uu-248499DiVA: diva2:799332