  The recently proposed generalized field method for solving the master
equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic
Lie algebras in 2-dimensions. The charge corresponding to BRST symmetry derived
from this solution in terms of the phase space variables by using the Noether
procedure, and the one found due to the BFV-method are compared and found to
coincide. $W_3$ algebra, formulated in terms of a continuous variable is
emploied in the mentioned gauge theory to construct a $W_3$ topological
gravity. Moreover, its gauge fixing is briefly discussed.
