An outline of shifted Poisson structures and deformation quantisation in derived differential geometry
Differential Geometry
2025-10-06 v4 Algebraic Geometry
Quantum Algebra
Abstract
We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and include existence and classification of various deformation quantisations.
Keywords
Cite
@article{arxiv.1804.07622,
title = {An outline of shifted Poisson structures and deformation quantisation in derived differential geometry},
author = {J. P. Pridham},
journal= {arXiv preprint arXiv:1804.07622},
year = {2025}
}
Comments
64 pp; v2 updated with more quantisation results; v3 correction in 3.4.3; v4 various corrections, updated results and expansions, 2 appendices added