  We consider the two-dimensional model of W3-gravity within Lagrangian
quantization methods for general gauge theories. We use the Batalin-Vilkovisky
formalism to study the arbitrariness in the realization of the gauge algebra.
We obtain a one-parametric non-analytic extension of the gauge algebra, and a
corresponding solution of the classical master equation, related via an
anticanonical transformation to a solution corresponding to an analytic
realization. We investigate the possibility of closed solutions of the
classical master equation in the Sp(2)-covariant formalism and show that such
solutions do not exist in the approximation up to the third order in ghost and
auxiliary fields.
