A characterization of groups of type $F_4$ arising from the first Tits construction

TL;DR

This paper demonstrates that algebraic groups of type F4, linked to Albert algebras via the first Tits construction, are uniquely identified by their g3 invariant, clarifying their classification.

Contribution

It establishes a unique correspondence between F4 groups from the first Tits construction and their g3 invariant, enhancing understanding of their structure.

Findings

F4 groups from the first Tits construction are uniquely determined by g3 invariant.

Provides a classification criterion for Albert algebras of type F4.

Clarifies the role of the g3 invariant in the structure of these algebraic groups.

Abstract

We show that algebraic groups of type $F_4$ (or equivalently Albert algebras) arising from the first Tits construction are determined uniquely by their $g_3$ invariant.