Abstract
An analogue of the Livernet–Loday operad for two compatible brackets, which is a flat deformation of the bi-Hamiltonian operad is constructed. The Livernet–Loday operad can be used to define ?-products and deformation quantization for Poisson structures. The constructed operad is used in the same way, introducing a definition of operadic deformation quantization of compatible Poisson structures.
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