##  [Lie's Theorem](/lies-theorem) 

  ##  [Lie's Theorem](https://algebra.quantumdictionary.io/lies-theorem-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

A theorem in the representation theory of Lie algebras which states that every finite-dimensional solvable Lie algebra of linear transformations over an algebraically closed field has a common eigenvector in the underlying vector space; equivalently, representations of solvable Lie algebras are triangularizable.