Automorphisms, derivations and gradings of the split quartic Cayley algebra

TL;DR

This paper investigates the automorphisms, derivations, and gradings of the split quartic Cayley algebra, a key algebraic structure used in constructing Lie algebras of type D4, providing detailed structural insights.

Contribution

It provides a comprehensive calculation of the automorphism group, derivation algebra, and gradings of the split quartic Cayley algebra, advancing understanding of its algebraic properties.

Findings

Determined the automorphism group of the algebra.

Computed the algebra of derivations.

Classified the gradings of the algebra.

Abstract

The split quartic Cayley algebra is a structurable algebra which has been used to give constructions of Lie algebras of type D4. Here, we calculate its group of automorphisms, its algebra of derivations and its gradings.