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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.06158 |
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| _version_ | 1866917699105325056 |
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| author | Thomas, Alexander |
| author_facet | Thomas, Alexander |
| contents | We describe new $q$-deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra $\mathfrak{sl}_2$ and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and $q$-deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to $q$-deformed Möbius transformations acting on the hyperbolic plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06158 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra Thomas, Alexander Quantum Algebra Mathematical Physics 17B66, 17B68 We describe new $q$-deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra $\mathfrak{sl}_2$ and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and $q$-deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to $q$-deformed Möbius transformations acting on the hyperbolic plane. |
| title | Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra |
| topic | Quantum Algebra Mathematical Physics 17B66, 17B68 |
| url | https://arxiv.org/abs/2308.06158 |