A canonical semi-classical star-product
  We study the Maurer-Cartan equation of the pre-Lie algebra of graphs controling the deformation theory of associative algebras and prove that there is a canonical solution within the class of graphs without circuits, without assuming the Jacobi identity. The proof is based on the unique factorization property of graph insertions. 
Lucian M. Ionescu (1), Papa A. Sissokho (1) ((1) Illinois State   University)