Remarks on the algebraic structure of (2,2) double forms

In this paper, we study the algebraic features of covariant tensors of valence four containing two blocks of skew indices. After a rather general treatment, we specialize ourselves to four-dimensional spacetimes and discuss several complementary aspects of these objects. In particular, we focus our attention on the corresponding invariant subspaces and generalize previous relations such as the Ruse–Lanczos identity, the Bel–Matte decomposition and the Lovelock-like quadratic identities. We conclude pointing out some possible applications of the formalisms.