Hall's identity

In mathematics, Hall's identity may be:
 * The Hall–Witt identity $$[x, y^{-1}, z]^y\cdot[y, z^{-1}, x]^z\cdot[z, x^{-1}, y]^x = 1$$
 * The Hall identity [ [x,y]2,z] = 0 for 2 by 2 matrices, showing that this is a polynomial identity ring
 * The Hall–Petresco identity for groups expressing xmym in terms of powers of elements of the descending central series.