Quantization of Poisson Hopf algebras
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866917373467951104 |
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| author | Pulmann, Ján Ševera, Pavol |
| author_facet | Pulmann, Ján Ševera, Pavol |
| contents | We describe a method for quantization of Poisson Hopf algebras in $\mathbb Q$-linear symmetric monoidal categories. It is compatible with tensor products and can also be used to produce braided Hopf algebras. The main idea comes from the fact that nerves of groups are symmetric simplicial sets. Nerves of Hopf algebras then turn out to be braided rather than symmetric and nerves of Poisson Hopf algebras to be infinitesimally braided. The problem is thus solved via the standard machinery of Drinfeld associators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_10616 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Quantization of Poisson Hopf algebras Pulmann, Ján Ševera, Pavol Quantum Algebra We describe a method for quantization of Poisson Hopf algebras in $\mathbb Q$-linear symmetric monoidal categories. It is compatible with tensor products and can also be used to produce braided Hopf algebras. The main idea comes from the fact that nerves of groups are symmetric simplicial sets. Nerves of Hopf algebras then turn out to be braided rather than symmetric and nerves of Poisson Hopf algebras to be infinitesimally braided. The problem is thus solved via the standard machinery of Drinfeld associators. |
| title | Quantization of Poisson Hopf algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/1906.10616 |