Abstract
We prove a quantization theorem of the algebra of polynomial functions on the dual ofa local Lie algebroid, by applying the results of the deformation quantization of twocoisotropic branes obtained by D. Calaque, G. Felder, A. Ferrario, and C. Rossi. in[CFFR09]. In this context the deformed algebras are the differential graded ChevalleyEilenberg algebra and the graded Universal Enveloping associative algebra of the trivialformal deformation of this local Lie algebroid. This generalize a famous theorem ofquantization of the dual of a Lie algebra obtained by M. Kontsevich in [Kon97] to thelocal Lie algebroids case.