LIE-ALGEBRA COHOMOLOGY AND GROUP-STRUCTURE OF GAUGE-THEORIES

We explicitly construct the adjoint operator of coboundary operator an d obtain the Hedge decomposition theorem and the Poincare duality for the Lie algebra cohomology of the infinite-dimensional gauge transform ation group. We show that the adjoint of the coboundary operator can b e identified with the BRST adjoint generator Q(+) for the Lie algebra cohomology induced by BRST generator Q. We also point out an interesti ng duality relation-Poincare duality-with respect to gauge anomalies a nd Wess-Zumino-Witten topological terms. We consider the consistent em bedding of the ERST adjoint generator ei into the relativistic phase s pace and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint Nother charge Q(+). (C) 1996 American Institute of Physics.