  The recently presented quantum antibrackets are generalized to quantum
Sp(2)-antibrackets. For the class of commuting operators there are true quantum
versions of the classical Sp(2)-antibrackets. For arbitrary operators we have a
generalized bracket structure involving higher Sp(2)-antibrackets. It is shown
that these quantum antibrackets may be obtained from generating operators
involving operators in arbitrary involutions. A recently presented quantum
master equation for operators, which was proposed to encode generalized quantum
Maurer-Cartan equations for arbitrary open groups, is generalized to the Sp(2)
formalism. In these new quantum master equations the generalized Sp(2)-brackets
appear naturally.
