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Hall's identity

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In mathematics, Hall's identity may be:

  • The Hall–Witt identity [ x , y − 1 , z ] y ⋅ [ y , z − 1 , x ] z ⋅ [ z , x − 1 , y ] x = 1 {\displaystyle ^{y}\cdot ^{z}\cdot ^{x}=1}
  • The Hall identity ,z] = 0 for 2 by 2 matrices, showing that this is a polynomial identity ring
  • The Hall–Petresco identity for groups expressing xy in terms of powers of elements of the descending central series.
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