  The background field method (BFM) for the Poisson Sigma Model (PSM) is
studied as an example of the application of the BFM technique to open gauge
algebras. The relationship with Seiberg-Witten maps arising in non-commutative
gauge theories is clarified. It is shown that the implementation of the BFM for
the PSM in the Batalin-Vilkovisky formalism is equivalent to the solution of a
generalized linearization problem (in the formal sense) for Poisson structures
in the presence of gauge fields. Sufficient conditions for the existence of a
solution and a constructive method to derive it are presented.
