BV AND BFV FORMULATION OF A GAUGE-THEORY OF QUADRATIC LIE-ALGEBRAS IN2D 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 qua dratic Lie algebras in two dimensions. The charge corresponding to BRS T symmetry derived from this solution in terms of the phase space vari ables 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 theo ry to construct a W-3 topological gravity. Moreover, its gauge fixing is briefly discussed.