Infinitesimal reduction-compatible star products are exactly bivector fields plus symmetric differential operators built from the characteristic distribution and the normal bundle, up to constraint equivalence.
The Strong Homotopy Structure of BRST Reduction
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abstract
In this paper we propose a reduction scheme for polydifferential operators phrased in terms of $L_\infty$-morphisms. The desired reduction $L_\infty$-morphism has been obtained by applying an explicit version of the homotopy transfer theorem. Finally, we prove that the reduced star product induced by this reduction $L_\infty$-morphism and the reduced star product obtained via the formal Koszul complex are equivalent.
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Infinitesimal Star Products Compatible with Coisotropic Reduction
Infinitesimal reduction-compatible star products are exactly bivector fields plus symmetric differential operators built from the characteristic distribution and the normal bundle, up to constraint equivalence.