Hamiltonian BRST quantization of a noncommutative non-Abelian gauge theory and its Seiberg-Witten map

We consider the Hamiltonian BRST quantization of a noncommutative non-Abelian gauge theory. The Seiberg-Witten map of all phase-space variables, including multipliers, ghosts, and their momenta, is given in first order in the noncommutative parameter theta. We show that there exists a complete consistency between the gauge structures of the original and mapped theories, derived in a canonical way, once we appropriately choose the map solutions.