Higher structures in Deformation Quantization
Presenting author: Ricardo Campos
To a smooth manifold one can associate the Lie algebras of multi-vector fields and multi-differential operators, where one can encode classical data (Poisson structures) and quantum data (star products). Relating these two led Kontsevich to his famous formality theorem that establishes the deformation quantization of Poisson manifolds. In this talk we will see that if the manifold is oriented, these Lie algebras admit richer Batalin-Vilkovisky (BV) algebra structures. I will introduce the relevant objects and show that this additional structure can be extended to a "homotopy BV" version of Kontsevich formality theorem and will explore applications of this result.
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