  Previously we have shown that open groups whose generators are in arbitrary
involutions may be quantized within a ghost extended framework in terms of the
nilpotent BFV-BRST charge operator. Here we show that they may also be
quantized within an Sp(2)-frame in which there are two odd anticommuting
operators called Sp(2)-charges. Previous results for finite open group
transformations are generalized to the Sp(2)-formalism. We show that in order
to define open group transformations on the whole ghost extended space we need
Sp(2)-charges in the nonminimal sector which contains dynamical Lagrange
multipliers. We give an Sp(2)-version of the quantum master equation with
extended Sp(2)-charges and a master charge of a more involved form, which is
proposed to represent the integrability conditions of defining operators of
connection operators and which therefore should encode the generalized quantum
  Maurer-Cartan equations for arbitrary open groups. General solutions of this
master equation are given in explicit form. A further extended Sp(2)-formalism
is proposed in which the group parameters are quadrupled to a supersymmetric
set and from which all results may be derived.
