2024/10/21 by Ekaterina Shemyakova, Shemyakova, Ekaterina, Yağmur Yılmaz +1
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Computer science #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics
paper · pdf · doi:10.48550/arxiv.2410.15664
openalex publication_date 2024/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that the chain map between the de Rham and Poisson complexes on a Poisson manifold also maps the Koszul bracket of differential forms into the Schouten bracket of multivector fields. In the generalized case of a P_∞-structure, where a Poisson bivector P is replaced by an arbitrary even multivector obeying [[P,P]]=0, an analog of the chain map and an L_∞-morphism from the higher Koszul brackets into the Schouten bracket are also known; however, they differ significantly in nature. In the present paper, we address the problem of quantizing this picture. In particular, we show that the L_∞-morphism is quantized into a single linear operator, which is a formal Fourier integral operator. This paper employs Voronov's thick morphism technique and quantum Mackenzie-Xu transformations in the framework of L_∞-algebroids.