The strong homotopy structure of BRST reduction (Q6137568)

This paper proposes a reduction scheme for equivariant polydifferential operators. Let us recall that in the theory of deformation quantization, the phase space is described by a Poisson manifold \(M\). Quantifying \(M\) refers to the construction of a star product on \(M\). Let us recall that the existence and the classification of star products in the setting of general Poisson manifolds are obtained by Kontsevich's formality theorem. The motivation of this paper is to investigate the compatibility of deformation and phase space reduction in the Poisson setting. The authors obtain the desired reduction \(L_{\infty}\)-morphism by applying an explicit version of the homotopy transfer theorem. Finally, the authors prove that the reduced star product induced by reduction coincides with the reduced star product obtained via the formal Koszul complex.