A formula for the second cohomology of two-step nilpotent groups
  In [5], the notion of polynomial cocycles is used to give an expression for the second cohomology of T-groups with coefficients in a torsion-free nilpotent module. We make this expression concrete in the case of a T-group G of nilpotency class <=2 and coefficients in a trivial G-module, using a Lie algebra associated to the group. This approach allows us to construct explicit cocycles representing the elements of the second cohomology group. 
Karel Dekimpe, Manfred Hartl and Sarah Wauters
math.GR math.AG