  Two essential properties of energy-momentum tensors T_{\mu\nu} are their
positivity and conservation. This is mathematically formalized by,
respectively, an energy condition, as the dominant energy condition, and the
vanishing of their divergence \nabla^\mu T_{\mu\nu}=0. The classical Bel and
Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors,
respectively, are rank-4 tensors. But they share these two properties with
energy momentum tensors: the Dominant Property (DP) and the divergence-free
property in the absence of sources (vacuum). Senovilla defined a universal
algebraic construction which generates a basic superenergy tensor T{A} from any
arbitrary tensor A. In this construction the seed tensor A is structured as an
r-fold multivector, which can always be done. The most important feature of the
basic superenergy tensors is that they satisfy automatically the DP,
independently of the generating tensor A. In a previous paper we presented a
more compact definition of T{A} using the r-fold Clifford algebra. This form
for the superenergy tensors allowed to obtain an easy proof of the DP valid for
any dimension. In this paper we include this proof. We explain which new
elements appear when we consider the tensor T{A} generated by a
non-degree-defined r-fold multivector A and how orthogonal Lorentz
transformations and bilinear observables of spinor fields are included as
particular cases of superenergy tensors. We find some sufficient conditions for
the seed tensor A, which guarantee that the generated tensor T{A} is
divergence-free. These sufficient conditions are satisfied by some physical
fields, which are presented as examples.
