Quantisation of derived Poisson structures

2017/08/01 by Pridham, J. P. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1708.00496

Abstract

We prove that every 0-shifted Poisson structure on a derived Artin n-stack admits a curved A_∞ deformation quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes, where it gives a DQ algebroid quantisation. Whereas the Kontsevich--Tamarkin approach to quantisation for smooth varieties hinges on invariance of the Hochschild complex under affine transformations, we instead exploit the observation that the Hochschild complex carries an anti-involution, and that such anti-involutive deformations of the complex of polyvectors are essentially unique. We also establish analogous statements for deformation quantisations in C^∞ and analytic settings.

Cited by

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

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