Classification of algebras of level two in the variety of nilpotent algebras and Leibniz algebras

摘要

This paper is devoted to the description of complex finite-dimensionalalgebras of level two. We obtain the classification of algebras of level two inthe variety of Leibniz algebras. It is shown that, up to isomorphism, thereexist three Leibniz algebras of level two, one of which is solvable, and two ofwhich are nilpotent. Moreover we describe all algebras of level two in thevariety of nilpotent algebras.