  The paper is devoted to the study of BRST charge in perturbed two dimensional
conformal field theory. The main goal is to write the operator equation
expressing the conservation law of BRST charge in perturbed theory in terms of
purely algebraic operations on the corresponding operator algebra, which are
defined via the OPE. The corresponding equations are constructed and their
symmetries are studied up to the second order in formal coupling constant. It
appears that the obtained equations can be interpreted as generalized
Maurer-Cartan ones. We study two concrete examples in detail: the bosonic
nonlinear sigma model and perturbed first order theory. In particular, we show
that the Einstein equations, which are the conformal invariance conditions for
both these perturbed theories, expanded up to the second order, can be
rewritten in such generalized Maurer-Cartan form.
