LIE-ALGEBRA COHOMOLOGY

We calculate the cohomology of the BRS operator s modulo an auxiliary differential operator t where both operators act on invariant polynomials in anticommuting variables Ci and commuting variables Xi.Ci and Xi transform according to the adjoint representation of the Lie algebra of a compact Lie group. The cohomology classes of s modulo t are related to the solutions of the consistency equations which ha have to be satisfied by anomalies of Yang-Mills theories. The present investigation completes the proof of the completeness and nontriviality of these solutions and, as a by-product, determines the cohomology of the underlying Lie algebra. © 1990.