Notation
A shorthand notation for anti-symmetrization is denoted by a pair of square brackets. For example, in arbitrary dimensions, for a order 2 covariant tensor M,
and for a order 3 covariant tensor T,
In any number of dimensions, these are equivalent to
More generally, irrespective of the number of dimensions, antisymmetrization over p indices may be expressed as
In the above,
is the generalized Kronecker delta of the appropriate order.
Read more about this topic: Antisymmetric Tensor