##  [Universal Enveloping Algebra](/universal-enveloping-algebra) 

  ##  [Universal Enveloping Algebra](https://algebra.quantumdictionary.io/universal-enveloping-algebra-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The associative unital algebra U(g) constructed from a Lie algebra g that is universal for Lie algebra representations into associative algebras; concretely obtained as the quotient of the tensor algebra T(g) by the ideal generated by elements x⊗y − y⊗x − [x,y].