LOCALLY REPRESENTABLE VARIETIES OF LIE-ALGEBRAS

A description is obtained for locally representable varieties of Lie algebras, i.e., varieties in which an arbitrary finitely generated algebra has a faithful representation of finite dimension over an extension of the ground field. In the case of an infinite field a variety of Lie algebras is locally representable if and only if the following two conditions hold:(1)is an identity in for some in; and(2) an arbitrary finitely generated algebra in lies in a product of nilpotent varieties, where if. © 1990 American Mathematical Society.