  We show that every (graded) derivation on the algebra of free quantum fields
and their Wick powers in curved spacetimes gives rise to a set of anomalous
Ward identities for time-ordered products, with an explicit formula for their
classical limit. We study these identities for the Koszul-Tate and the full
BRST differential in the BV-BRST formulation of perturbatively interacting
quantum gauge theories, and clarify the relation to previous results. In
particular, we show that the quantum BRST differential, the quantum antibracket
and the higher-order anomalies form an $L_\infty$ algebra. The defining
relations of this algebra ensure that the gauge structure is well-defined on
cohomology classes of the quantum BRST operator, i.e., observables.
Furthermore, we show that one can determine contact terms such that also the
interacting time-ordered products of multiple interacting fields are well
defined on cohomology classes. An important technical improvement over previous
treatments is the fact that all our relations hold off-shell and are
independent of the concrete form of the Lagrangian, including the case of open
gauge algebras.
