##  [Failure of the PBW Property](/index.php/failure-pbw-property) 

  ##  [Failure of the PBW Property](https://algebra.quantumdictionary.io/failure-pbw-property-0) 

  

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**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A situation in which a filtered algebra does not satisfy the Poincaré–Birkhoff–Witt (PBW) property, meaning its associated graded algebra differs from the expected symmetric or tensor algebra and the standard PBW basis or deformation-theoretic identifications fail to hold.