Even (Odd) Roots and Simple Leibniz Algebras with Lie Factor $s{\ell }_2$

Abstract

We introduce 3-irreducible modules, even roots and odd roots for Leibniz algebras, produce a basis for a root space of a Leibniz algebra with a semisimple Lie factor, and classify finite dimensional simple Leibniz algebras with Lie factor $s{\ell }_2$.

9 pages