Classification of realizations of Lie algebras of vector fields on circle
UDC 517.986.5 The realizations of finite-dimensional Lie algebras of smooth tangent vector fields on circle are described.The ``canonical'' realizations of two-dimensional noncommutative algebra, as well as the algebra $\mathfrak{sl}(2,\mathbb R)$ are constructed. It is shown that...
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| Date: | 2022 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6270 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.986.5
The realizations of finite-dimensional Lie algebras of smooth tangent vector fields on circle are described.The ``canonical'' realizations of two-dimensional noncommutative algebra, as well as the algebra $\mathfrak{sl}(2,\mathbb R)$ are constructed. It is shown that any realization of these algebras by smooth vector fields is reduced to one of a ``canonical'' realization by piecewise-smooth global transformations of circle onto itself.Formulas for calculating the number of non-equivalent realizations are obtained. |
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| DOI: | 10.37863/umzh.v74i3.6270 |