Even (Odd) Roots and Simple Leibniz Algebras with Lie Factor $s\ell_2$

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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

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