  A new type of quantum master equation is presented which is expressed in
terms of a recently introduced quantum antibracket. The equation involves only
two operators: an extended nilpotent BFV-BRST charge and an extended ghost
charge. It is proposed to determine the generalized quantum Maurer-Cartan
equations for arbitrary open groups. These groups are the integration of
constraints in arbitrary involutions. The only condition for this is that the
constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST
charge. The proposal is verified at the quasigroup level. The integration
formulas are also used to construct a generating operator for quantum
antibrackets of operators in arbitrary involutions.
