Gradings on Algebras over Algebraically Closed Fields

Abstract

The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra $\mathcal{A}$ over an algebraically closed field $\mathbb{F}$ such that the group scheme of automorphisms $\mathop{\mathbf{Aut}}\nolimits (\mathcal{A})$ is smooth is shown to be equivalent to the corresponding problem for $\mathcal{A}_{\mathbb{K}} = \mathcal{A}\otimes _{\mathbb{F}}\mathbb{K}$ for any algebraically closed field extension $\mathbb{K}$.