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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.sub(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

BV AND BFV FORMULATION OF A GAUGE THEORY OF QUADRATIC LIE ALGEBRAS IN 2D AND A CONSTRUCTION OF W3 TOPOLOGICAL GRAVITY

BV AND BFV FORMULATION OF A GAUGE THEORY OF QUADRATIC LIE ALGEBRAS IN 2D AND A CONSTRUCTION OF W₃ TOPOLOGICAL GRAVITY