The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂)
Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension Δ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between Δ and the quantum algebra Uq(sl₂). Our main result is an algebra injection from Δ into a r...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147989 |
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| Cite this: | The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
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Terwilliger, P. 2019-02-16T12:45:20Z 2019-02-16T12:45:20Z 2011 The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D80; 33D45 http://dx.doi.org/10.3842/SIGMA.2011.099 https://nasplib.isofts.kiev.ua/handle/123456789/147989 Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension Δ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between Δ and the quantum algebra Uq(sl₂). Our main result is an algebra injection from Δ into a relative of Uq(sl₂); the relative is obtained from Uq(sl₂) by adjoining three mutually commuting indeterminates. We describe the injection using the equitable presentation of Uq(sl₂). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) |
| spellingShingle |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) Terwilliger, P. |
| title_short |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) |
| title_full |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) |
| title_fullStr |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) |
| title_full_unstemmed |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) |
| title_sort |
universal askey-wilson algebra and the equitable presentation of uq(sl₂) |
| author |
Terwilliger, P. |
| author_facet |
Terwilliger, P. |
| publishDate |
2011 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension Δ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between Δ and the quantum algebra Uq(sl₂). Our main result is an algebra injection from Δ into a relative of Uq(sl₂); the relative is obtained from Uq(sl₂) by adjoining three mutually commuting indeterminates. We describe the injection using the equitable presentation of Uq(sl₂).
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147989 |
| citation_txt |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
| work_keys_str_mv |
AT terwilligerp theuniversalaskeywilsonalgebraandtheequitablepresentationofuqsl2 AT terwilligerp universalaskeywilsonalgebraandtheequitablepresentationofuqsl2 |
| first_indexed |
2025-12-07T20:46:32Z |
| last_indexed |
2025-12-07T20:46:32Z |
| _version_ |
1850883852194545664 |