Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917300967309312 |
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| author | Esposito, Chiara Rivezzi, Andrea Schnitzer, Jonas Weber, Thomas |
| author_facet | Esposito, Chiara Rivezzi, Andrea Schnitzer, Jonas Weber, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras Esposito, Chiara Rivezzi, Andrea Schnitzer, Jonas Weber, Thomas Quantum Algebra Category Theory Rings and Algebras Representation Theory 18M15, 16T25, 13D10 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. |
| title | Quantization of infinitesimal braidings and pre-Cartier quasi-bialgebras |
| topic | Quantum Algebra Category Theory Rings and Algebras Representation Theory 18M15, 16T25, 13D10 |
| url | https://arxiv.org/abs/2505.17729 |