  In 1993, Lian-Zuckerman constructed two cohomology operations on the BRST
complex of a conformal vertex algebra with central charge 26. They gave
explicit generators and relations for the cohomology algebra equipped with
these operations in the case of the c=1 model. In this paper, we describe
another such example, namely, the semi-infinite Weil complex of the Virasoro
algebra. The semi-infinite Weil complex of a tame Z-graded Lie algebra was
defined in 1991 by Feigin-Frenkel, and they computed the linear structure of
its cohomology in the case of the Virasoro algebra. We build on this result by
giving an explicit generator for each non-zero cohomology class, and describing
all algebraic relations in the sense of Lian-Zuckerman, among these generators.
