Definition of brackets in index notation I've come across the notation $B_{[ij]}$ and $\partial_{[k}B_{ij]}$.  What do these notations mean?
The text says that $[ij] := (ij-ij)/2$, but doesn't the $ij$ just specify the which component of the tensor $B$ that we're discussing?  I don't see how you can do math on the indices like that.  The second notation with the brackets on both the derivative operator and $B$ looks even more confusing.

What they mean is that
$$B_{[ij]}=\frac 12 \left(B_{ij}-B_{ji}\right)$$
and
$$\partial_{[k}B_{ij]}=\frac 16 \left(\partial_{k}B_{ij}+\partial_{i}B_{jk}+\partial_{j}B_{ki}-\partial_{k}B_{ji}-\partial_{j}B_{ik}-\partial_{i}B_{kj}\right).$$
