  The $\Delta$-operator of the Batalin-Vilkovisky formalism is the Hamiltonian
BRST charge of Abelian shift transformations in the ghost momentum
representation. We generalize this $\Delta$-operator, and its associated
hierarchy of antibrackets, to that of an arbitrary non-Abelian and possibly
open algebra of any rank. We comment on the possible application of this
formalism to closed string field theory.
