  The Bel-Robinson tensor is analyzed as a linear map on the space of the
traceless symmetric tensors. This study leads to an algebraic classification
that refines the usual Petrov-Bel classification of the Weyl tensor. The new
classes correspond to degenerate type I space-times which have already been
introduced in literature from another point of view. The Petrov-Bel types and
the additional ones are intrinsically characterized in terms of the sole
Bel-Robinson tensor, and an algorithm is proposed that enables the different
classes to be distinguished. Results are presented that solve the problem of
obtaining the Weyl tensor from the Bel-Robinson tensor in regular cases.
