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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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2018
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209438 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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