Deformation quantisation for (-2)-shifted symplectic structures

2018/09/28 by J. P. Pridham, Pridham, J. P. · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1809.11028

openalex publication_date 2018/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a notion of E_-1 quantisation of (-2)-shifted Poisson structures on derived algebraic stacks, depending on a flat right connection on the structure sheaf, as solutions of a quantum master equation. We then parametrise E_-1 quantisations of (-2)-shifted symplectic structures by constructing a map to power series in de Rham cohomology. For derived schemes, we show that these quantisations give rise to classes in Borel--Moore homology, and for a large class of examples we show that the classes are closely related to Borisov--Joyce invariants.

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• Deformation quantisation of exact shifted symplectic structures, with an application to vanishing cycles

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