Connection (algebraic framework)

<p>Geometry of <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum systems</a> (e.g.,
<a href="/facts/Noncommutative_geometry/WSwggL1p">noncommutative geometry</a> and <a href="/facts/Supergeometry/ucKekXjf">supergeometry</a>) is mainly
phrased in algebraic terms of <a href="/facts/Module_(mathematics)/jP0LIhFL">modules</a> and
<a href="/facts/Algebras/8T8ulWJb">algebras</a>. Connections on modules are
generalization of a linear <a href="/facts/Connection_(vector_bundle)/Rxv5S2Af">connection</a> on a smooth <a href="/facts/Vector_bundle/cXACAa1I">vector bundle</a> 
  
    
      
        E
        →
        X
      
    
    {\displaystyle E\to X}
  
 written as a <a href="/facts/Koszul_connection/Rxv5S2Af">Koszul connection</a> on the

C
          
            ∞
          
        
        (
        X
        )
      
    
    {\displaystyle C^{\infty }(X)}
  
-module of sections of 
  
    
      
        E
        →
        X
      
    
    {\displaystyle E\to X}
  
.
</p>

Connection (algebraic framework) open-in-new

Connection (algebraic framework)