  Recently M. Kontsevich found a combinatorial formula defining a star-product
of deformation quantization for any Poisson manifold. Kontsevich's formula has
been reinterpreted physically as quantum correlation functions of a topological
sigma model for open strings as well as in the context of D-branes in flat
backgrounds with a Neveu-Schwarz B-field. Here the corresponding Kontsevich's
formula for the dual of a Lie algebra is derived in terms of the formalism of
D-branes on group manifolds. In particular we show that that formula is encoded
at the two-point correlation functions of the Wess-Zumino-Witten effective
theory with Dirichlet boundary conditions. The B-field entering in the
formalism plays an important role in this derivation.
