The Classifying Lie Algebroid of a Geometric Structure I: Classes of   Coframes
  We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartan's realization problem that applies to both the local and the global versions of this problem. 
Rui Loja Fernandes and Ivan Struchiner
math.DG