The BRST complex, as it arizes in the pure spinor string theory, involves a representation
of the algebra (the algebra of covariant derivatives).
The BRST operator acts on the space of functions of , taking values
in :
(23)
It acts on in the following way:
(24)
The exactness of the sequence (18) implies that the cohomology
of (24) in fact coincides with the Lie algebra cohomology of
the Lie algebra (22):
