ON SEVERAL VARIETIES OF LEIBNIZ ALGEBRAS

Abstract

The paper is devoted to two new results concerning varieties of Leibniz alge
bras. In case of prime characteristic p we construct an example of a non-nilpo
tent variety of Leibniz algebras with Engel condition. In case of field of character
istic zero we obtain a new result concerning the space of multilinear components
of the variety of left-nilpotent Leibniz algebra of class three.