Separating G_2-invariants of several octonions

TL;DR

This paper studies the invariants under the G_2 group action on multiple copies of octonion algebras over fields of different characteristics, providing minimal generating and separating sets.

Contribution

It introduces explicit minimal generating and separating sets for G_2-invariants of multiple octonion copies in both characteristic two and odd characteristic fields.

Findings

Explicit minimal separating sets in characteristic two.

Minimal generating sets in odd characteristic.

Advances understanding of G_2-invariants in octonion algebras.

Abstract

We describe separating G_2-invariants of several copies of the algebra of octonions over an algebraically closed field of characteristic two. We also obtain a minimal separating and a minimal generating set for G_2-invariants of several copies of the algebra of octonions in case of a field of odd characteristic.