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 x^my^m in terms of powers of elements of the descending central series.