The Delta-operator of the Batalin-Vilkovisky formalism is the Hamilton
ian 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 po
ssibly open algebra of any rank. We comment on the possible applicatio
n of this formalism to closed string field theory.