Hall's identity

In mathematics, Hall's identity may be:

• The Hall–Witt identity [math]\displaystyle{ [x, y^{-1}, z]^y\cdot[y, z^{-1}, x]^z\cdot[z, x^{-1}, y]^x = 1 }[/math]
• 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.

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