Integrable module

<p>In algebra, an integrable module (or integrable representation) of a <a href="/facts/Kac%25E2%2580%2593Moody_algebra/N8caXyvw">Kac–Moody algebra</a> 
  
    
      
        
          
            g
          
        
      
    
    {\displaystyle {\mathfrak {g}}}
  
 (a certain <a href="/facts/Infinite-dimensional_Lie_algebra/NUSj3xlQ">infinite-dimensional Lie algebra</a>) is a <a href="/facts/Representation_of_a_Lie_algebra/aaxnMxCR">representation</a> of 
  
    
      
        
          
            g
          
        
      
    
    {\displaystyle {\mathfrak {g}}}
  
 such that (1) it is a sum of weight spaces and (2) the Chevalley generators 
  
    
      
        
          e
          
            i
          
        
        ,
        
          f
          
            i
          
        
      
    
    {\displaystyle e_{i},f_{i}}
  
 of 
  
    
      
        
          
            g
          
        
      
    
    {\displaystyle {\mathfrak {g}}}
  
 are locally nilpotent. For example, the <a href="/facts/Adjoint_representation_of_a_Lie_algebra/bWG4c2su">adjoint representation</a> of a Kac–Moody algebra is <a href="/facts/Integrable/Crgzjw6G">integrable</a>.
</p>

Integrable module open-in-new

Integrable module