BV AND BFV FORMULATION OF A GAUGE-THEORY OF QUADRATIC LIE-ALGEBRAS IN 2D AND A CONSTRUCTION OF W-3 TOPOLOGICAL GRAVITY

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 two 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 exploit in the mentioned gauge theory to construct a W-3 topological gravity. Moreover, its gauge fixing is briefly discussed.