  Open groups whose generators are in arbitrary involutions may be quantized
within a ghost extended framework in terms of a nilpotent BFV-BRST charge
operator. Previously we have shown that generalized quantum Maurer-Cartan
equations for arbitrary open groups may be extracted from the quantum
connection operators and that they also follow from a simple quantum master
equation involving an extended nilpotent BFV-BRST charge and a master charge.
Here we give further details of these results. In addition we establish the
general structure of the solutions of the quantum master equation. We also
construct an extended formulation whose properties are determined by the
extended BRST charge in the master equation.
