  We show that every algebraic group scheme over a field with at least 8
elements can be realized as the group of automorphisms of a nonassociative
algebra. This is only a modest improvement of the theorem of Gordeev and Popov
(2003), but it allows us to give a new characterization of algebraic Lie
algebras and to simplify the standard descriptions of Mumford--Tate domains and
Shimura varieties as moduli spaces. Once the original argument of Gordeev and
Popov has been rewritten in the language of schemes, we find that it also
applies to algebraic groups over discrete valuation rings.
