This matrix is antisymmetric:

Declare a rank-4 array to be antisymmetric in three slots:

Then any transposition involving those slots is equivalent to the original tensor, perhaps up to a sign:

Antisymmetry in all slots of a symbolic array:

It can also be specified as follows:

Antisymmetry in the given slots of a symbolic array:

Antisymmetric[{}] and Antisymmetric[{s}] are representations of the absence of symmetry:

Such cases are canonicalized to an empty list of generators:

Specify the symmetry of a symmetrized array:

Specify the symmetry of a symbolic array:

Symmetrize several slots of an array:

Detect antisymmetric matrices:

An antisymmetric tensor can also be specified by providing explicit generators with phase :

The Wolfram Language automatically detects the equivalence:

Overlapping sets of antisymmetric slots give full antisymmetry over all those slots:

Non-overlapping sets do not give full antisymmetry. The resulting symmetry is described using generators:

Dimensions must coincide in all symmetry slots: