  In this paper, first we introduce the notion of a nonabelian embedding tensor
on the 3-Lie algebra. Then, we introduce the notion of a 3-Leibniz-Lie algebra,
which is the underlying algebraic structure of a nonabelian embedding tensor on
the 3-Lie algebra, and can also be viewed as a nonabelian generalization of a
3-Leibniz algebra. Next we develop the cohomology of nonabelian embedding
tensors on 3-Lie algebras with coefficients in a suitable representation and
use the first cohomology group to characterize infinitesimal deformations.
Finally, we investigate nonabelian embedding tensors on 3-Lie algebras induced
by Lie algebras.
