##  [Jacobi Identity](/jacobi-identity) 

  ##  [Jacobi Identity](https://puremath.quantumdictionary.io/jacobi-identity-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An identity for a bilinear bracket [·,·] on an algebraic structure stating that [x,[y,z]]+[y,[z,x]]+[z,[x,y]]=0 for all elements x,y,z, encoding cyclic symmetry required for Lie-type structures.