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arXiv · 2505.17729

Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras

Chiara Esposito·Andrea Rivezzi·Jonas Schnitzer·Thomas Weber
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Abstract

In this paper we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the non-symmetric case. The algebraic counterpart of these categories is the notion of a pre-Cartier quasi-bialgebra, which extends the well-known notion of quasitriangular quasi-bialgebra given by Drinfeld. Our result implies that one can quantize the infinitesimal $\mathcal{R}$-matrix of any Cartier quasi-bialgebra. We further discuss the emerging concepts of infinitesimal quantum Yang-Baxter equation and Cartier ring, the latter containing braid groups with additional generators that correspond to infinitesimal braidings. Explicit deformations of the representation categories of the gauge deformed quasitriangular quasi-bialgebras $E(n)$ are provided.

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Chiara Esposito, Andrea Rivezzi, Jonas Schnitzer, Thomas Weber. 2026-03-01. Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras. https://doi.org/10.1112/jlms.70494

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