On the structure of graded 3-Leibniz algebras

Abstract

– We study the structure of a “3-Leibniz algebra” T graded by an arbitrary abelian group G, which is considered of arbitrary dimension and over an arbitrary base field . We show that T is of the form with a linear subspace of the homogeneous component associated to the unit element 1 in G, and every Ij is a well described graded ideal of T, satisfying if In the case of T being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.