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Composition Algebras and Outer Automorphisms of Algebraic Groups
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.ORCID iD: 0000-0002-0182-6205
(English)Article in journal (Other academic) Submitted
Abstract [en]

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.

Keyword [en]
Composition algebras, algebraic groups, outer automorphisms, triality
National Category
URN: urn:nbn:se:uu:diva-248499OAI: oai:DiVA.org:uu-248499DiVA: diva2:799332
Available from: 2015-03-30 Created: 2015-03-30 Last updated: 2015-04-07

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Alsaody, Seidon
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