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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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147989 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1479892019-02-17T01:24:37Z The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) Terwilliger, P. 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). 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147989 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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). |
| format |
Article |
| author |
Terwilliger, P. |
| spellingShingle |
Terwilliger, P. The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Terwilliger, P. |
| author_sort |
Terwilliger, P. |
| title |
The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) |
| 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) |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT terwilligerp theuniversalaskeywilsonalgebraandtheequitablepresentationofuqsl2 AT terwilligerp universalaskeywilsonalgebraandtheequitablepresentationofuqsl2 |
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2023-05-20T17:28:20Z |
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2023-05-20T17:28:20Z |
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1796153367568842752 |