Triality and etale algebras

TL;DR

This paper explores the concept of triality in relation to etale algebras, specifically classifying octic etale algebras with trivial discriminant and their connection to trialitarian automorphisms and Galois cohomology.

Contribution

It provides a classification of octic etale algebras with trivial discriminant containing quartic subalgebras using Galois cohomology and examines triality automorphisms in this context.

Findings

Classification of octic etale algebras with trivial discriminant

Connection between triality automorphisms and Galois cohomology

Insights into automorphisms of order 3 of D4 Dynkin diagram

Abstract

Trialitarian automorphisms are related to automorphisms of order 3 of the Dynkin diagram of type D4. Octic etale algebras with trivial discriminant, containing quartic subalgebras, are classified by Galois cohomology with value in the Weyl group of type D4. This paper discusses triality for such étale extensions.