Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
In our earlier article [Lett. Math. Phys. 107 (2017), 475-503], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every deformation quantization leads to a Drinfeld twist of the associative bialgebroid...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209438 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures / S. Meljanac, Z. Škoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. |
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Meljanac, S. Škoda, Z. 2025-11-21T18:52:03Z 2018 Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures / S. Meljanac, Z. Škoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D55; 16S30; 16T05 arXiv: 1605.01376 https://nasplib.isofts.kiev.ua/handle/123456789/209438 https://doi.org/10.3842/SIGMA.2018.026 In our earlier article [Lett. Math. Phys. 107 (2017), 475-503], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every deformation quantization leads to a Drinfeld twist of the associative bialgebroid of h-adic series of differential operators on a fixed Poisson manifold. In the case of linear Poisson structures, the twisted bialgebroid essentially coincides with our construction. Using our explicit description of the Hopf algebroid, we compute the corresponding Drinfeld twist explicitly as a product of two exponential expressions. S.M. has been supported by the Croatian Science Foundation under the Project no. IP-2014-09-9582 and the H2020 Twinning project no. 692194 “RBI-T-WINNING”. Z.Š. has been partly supported by grant no. 18-00496S of the Czech Science Foundation. We thank A. Borowiec for his remarks on the paper and M. Stojić for his remarks on Sections 1 and 2. We thank the referees for bringing to our attention numerous constructive suggestions, which helped extend and improve the article significantly. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures |
| spellingShingle |
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures Meljanac, S. Škoda, Z. |
| title_short |
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures |
| title_full |
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures |
| title_fullStr |
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures |
| title_full_unstemmed |
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures |
| title_sort |
hopf algebroid twists for deformation quantization of linear poisson structures |
| author |
Meljanac, S. Škoda, Z. |
| author_facet |
Meljanac, S. Škoda, Z. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
In our earlier article [Lett. Math. Phys. 107 (2017), 475-503], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every deformation quantization leads to a Drinfeld twist of the associative bialgebroid of h-adic series of differential operators on a fixed Poisson manifold. In the case of linear Poisson structures, the twisted bialgebroid essentially coincides with our construction. Using our explicit description of the Hopf algebroid, we compute the corresponding Drinfeld twist explicitly as a product of two exponential expressions.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209438 |
| citation_txt |
Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures / S. Meljanac, Z. Škoda // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 25 назв. — англ. |
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AT meljanacs hopfalgebroidtwistsfordeformationquantizationoflinearpoissonstructures AT skodaz hopfalgebroidtwistsfordeformationquantizationoflinearpoissonstructures |
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2025-11-24T07:13:53Z |
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2025-11-24T07:13:53Z |
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1850885965781925888 |