  In an n dimensional vector space, any tensor which is antisymmetric in k>n
arguments must vanish; this is a trivial consequence of the limited number of
dimensions. However, when other possible properties of tensors, for example
trace-freeness, are taken into account, such identities may be heavily
disguised. Tensor identities of this kind were first considered by Lovelock,
and later by Edgar and Hoeglund.
  In this paper we continue their work. We obtain dimensionally dependent
identities for highly structured expressions of products of (2,2)-forms. For
tensors possessing more symmetries, such as block symmetry W_{abcd} = W_{cdab},
or the first Bianchi identity W_{a[bcd]} = 0, we derive identities for less
structured expressions.
  These identities are important tools when studying super-energy tensors, and,
in turn, deriving identities for them. As an application we are able to show
that the Bel-Robinson tensor, the super-energy tensor for the Weyl tensor,
satisfies the equation T_{abcy}T^{abcx} = 1/4g^{x}_{y}T_{abcd}T^{abcd} in four
dimensions, irrespective of the signature of the space.
