Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane
A complete list of Uq(sl₂)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the Uq(sl₂)-module algebra structur...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106653 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane / S. Duplij, S. Sinel’shchikov // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 4. — С. 406-430. — Бібліогр.: 13 назв. — англ. |
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Duplij, S. Sinel’shchikov, S. 2016-10-01T17:21:57Z 2016-10-01T17:21:57Z 2010 Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane / S. Duplij, S. Sinel’shchikov // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 4. — С. 406-430. — Бібліогр.: 13 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106653 A complete list of Uq(sl₂)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the Uq(sl₂)-module algebra structures are discussed. One of the authors (S.D.) is thankful to Yu. Bespalov, J. Cuntz, B. Dragovich, J. Fuchs, A. Gavrilik, H. Grosse, D. Gurevich, J. Lukierski, M. Pavlov, H. Steinacker, Z. Rakic, W. Werner, and S. Woronowicz for fruitful discussions. Also he is grateful to the Alexander von Humboldt Foundation for valuable support as well as to J. Cuntz for kind hospitality at the Mathematisches Institut, Universit¨at M¨unster, where this paper was finalized. Both authors would like to express their gratitude to D. Shklyarov who attracted their attention to the fact that the results of this work were actually valid for q not being a root of unit, rather than for 0 < q < 1. We are also grateful to the referee who pointed out some inconsistencies in a previous version of the paper. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane |
| spellingShingle |
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane Duplij, S. Sinel’shchikov, S. |
| title_short |
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane |
| title_full |
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane |
| title_fullStr |
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane |
| title_full_unstemmed |
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane |
| title_sort |
classification of uq(sl₂)-module algebra structures on the quantum plane |
| author |
Duplij, S. Sinel’shchikov, S. |
| author_facet |
Duplij, S. Sinel’shchikov, S. |
| publishDate |
2010 |
| language |
English |
| container_title |
Журнал математической физики, анализа, геометрии |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
A complete list of Uq(sl₂)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the Uq(sl₂)-module algebra structures are discussed.
|
| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/106653 |
| citation_txt |
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane / S. Duplij, S. Sinel’shchikov // Журнал математической физики, анализа, геометрии. — 2010. — Т. 6, № 4. — С. 406-430. — Бібліогр.: 13 назв. — англ. |
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2025-12-07T15:13:47Z |
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2025-12-07T15:13:47Z |
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