LAUSR

Abstract We introduce and describe the class of split 3-Leibniz algebras as the natural extension of the class of split Lie algebras, split Leibniz algebras, split Lie triple systems and split 3-Lie algebras. More precisely, we show that any of such split 3-Leibniz algebras T is of the form T = U + ∑ j I j , with U a subspace of the 0-root space T 0 , and I j an ideal of T satisfying [ T , I j , I k ] + [ I j , T , I k ] + [ I j , I k , T ] = 0 for j ≠ k . Moreover, if T is of maximal length, we characterize the simplicity of T in terms of a connectivity property in its set of non-zero roots.