We study the structure of a “3-Leibniz algebra”Tgraded by an arbitrary abeliangroupG, which is considered of arbitrary dimension and over an arbitrary basefieldF. We show thatTis of the formT=U⊕∑jIj,withUa linear subspaceofT1, the homogeneous component associated to the unit element 1 inG,andeveryIjis a well described graded ideal ofT, satisfying[Ij,T,Ik]=[Ij,Ik,T]=[T,Ij,Ik]=0,ifj=k. In the case ofTbeing of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.
