Infinitesimal 2-braidings from 2-shifted Poisson structures

Kemp, Cameron; Laugwitz, Robert; Schenkel, Alexander

Abstract

It is shown that every 2-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra A defines a very explicit infinitesimal 2-braiding on the homotopy 2-category of the symmetric monoidal dg-category of finitely generated semi-free A-dg-modules. This provides a concrete realization, to first order in the deformation parameter ħ, of the abstract deformation quantization results in derived algebraic geometry due to Calaque, Pantev, Toën, Vaquié and Vezzosi. Of particular interest is the case when A is the Chevalley-Eilenberg algebra of a Lie N-algebra, where the braided monoidal deformations developed in this paper may be interpreted as candidates for representation categories of ‘higher quantum groups’.

Citation

Kemp, C., Laugwitz, R., & Schenkel, A. (2025). Infinitesimal 2-braidings from 2-shifted Poisson structures. Journal of Geometry and Physics, 212, Article 105456. https://doi.org/10.1016/j.geomphys.2025.105456

• Journal Article Type: Article
• Acceptance Date: Feb 16, 2025
• Online Publication Date: Feb 18, 2025
• Publication Date: 2025-06
• Deposit Date: Feb 27, 2025
• Publicly Available Date: Feb 27, 2025
• Journal: Journal of Geometry and Physics
• Print ISSN: 0393-0440
• Electronic ISSN: 0393-0440
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 212
• Article Number: 105456
• DOI: https://doi.org/10.1016/j.geomphys.2025.105456
• Keywords: Derived algebraic geometry, Shifted Poisson structures, Lie N-algebras, Deformation quantization, Braided monoidal 2-categories
• Public URL: https://nottingham-repository.worktribe.com/output/45857482
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0393044025000403?via%3Dihub