Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra
We describe new -deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra ₂, and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and -deformed rational numbers defined by Morier-Genoud and Ov...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212254 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra. Alexander Thomas. SIGMA 20 (2024), 053, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862610669716635648 |
|---|---|
| author | Thomas, Alexander |
| author_facet | Thomas, Alexander |
| citation_txt | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra. Alexander Thomas. SIGMA 20 (2024), 053, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We describe new -deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra ₂, and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and -deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to -deformed Möbius transformations acting on the hyperbolic plane.
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| first_indexed | 2026-03-14T06:40:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212254 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T06:40:45Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Thomas, Alexander 2026-02-03T07:54:57Z 2024 Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra. Alexander Thomas. SIGMA 20 (2024), 053, 16 pages 1815-0659 2020 Mathematics Subject Classification: 35A01; 65L10; 65L12; 65L20; 65L70 arXiv:2308.06158 https://nasplib.isofts.kiev.ua/handle/123456789/212254 https://doi.org/10.3842/SIGMA.2024.053 We describe new -deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra ₂, and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and -deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to -deformed Möbius transformations acting on the hyperbolic plane. I warmly thank Valentin Ovsienko and Sophie Morier-Genoud for inspiration, many suggestions, and fruitful exchanges, and Peter Smillie and Vladimir Fock for helpful discussions. I also thank the anonymous referees for their remarks improving the paper. I gratefully acknowledge support from the University of Heidelberg, where this work has been carried out, in particular under ERC-Advanced Grant 101018839 and Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 281071066 - TRR 191. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra Article published earlier |
| spellingShingle | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra Thomas, Alexander |
| title | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra |
| title_full | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra |
| title_fullStr | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra |
| title_full_unstemmed | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra |
| title_short | Infinitesimal Modular Group: -Deformed ₂ and Witt Algebra |
| title_sort | infinitesimal modular group: -deformed ₂ and witt algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212254 |
| work_keys_str_mv | AT thomasalexander infinitesimalmodulargroupdeformed2andwittalgebra |