  A BV algebra is a formal framework within which the BV quantization algorithm
is implemented. In addition to the gauge symmetry, encoded in the BV master
equation, the master action often exhibits further global symmetries, which may
be in turn gauged. We show how to carry this out in a BV algebraic set up.
Depending on the nature of the global symmetry, the gauging involves coupling
to a pure ghost system with a varying amount of ghostly supersymmetry. Coupling
to an N=0 ghost system yields an ordinary gauge theory whose observables are
appropriately classified by the invariant BV cohomology. Coupling to an N=1
ghost system leads to a topological gauge field theory whose observables are
classified by the equivariant BV cohomology. Coupling to higher $N$ ghost
systems yields topological gauge field theories with higher topological
symmetry. In the latter case, however, problems of a completely new kind
emerge, which call for a revision of the standard BV algebraic framework.
