Characterize the projected non-commutative BV structure

Investigate the algebraic properties of the projected deformation-quantised complex of functions on the degree-2 QP-manifold, and determine its possible relation to non-commutative Batalin–Vilkovisky algebras, with particular attention to the second-order component of the projected differential as a candidate BV Laplacian.

Background

The deformation-quantised QP-manifold yields a strict differential graded Lie algebra before projection to the momentum-independent subalgebra. After projection, the differential is no longer an inner derivation and fails to satisfy the Leibniz rule by an explicitly controlled term. The authors observe that the second-order part of this differential resembles a BV Laplacian and that the deformed master equation has the form of a quantum master equation.

The paper therefore leaves unresolved whether the projected structure constitutes, or can be related to, a non-commutative BV algebra and what its precise algebraic properties are.