Our stratedy
Interpret the standard BRST complex as a Lie algebra cohomology complex for some infinite-dimensional Lie algebra; actually we will need the so-called relative Lie algebra cohomology
This relative cohomology can be interpreted as the cohomology (usual, not relative; and with trivial coefficients) of some ideal, which is defined similarly to the ideal
of the Maxwell theory
We can do this for bothand flat space.