The Universal Askey-Wilson Algebra
In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call Δ the universal Askey-Wilso...
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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
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/123456789/147390 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 66 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147390 |
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irk-123456789-1473902019-02-15T01:23:16Z The Universal Askey-Wilson Algebra Terwilliger, P. In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call Δ the universal Askey-Wilson algebra. We give a faithful action of the modular group PSL₂(Z) on Δ as a group of automorphisms. We give a linear basis for Δ. We describe the center of Δ and the 2-sided ideal Δ[Δ,Δ]Δ. We discuss how Δ is related to the q-Onsager algebra. 2011 Article The Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 66 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D80; 33D45 http://dspace.nbuv.gov.ua/handle/123456789/147390 DOI:10.3842/SIGMA.2011.069 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 |
In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call Δ the universal Askey-Wilson algebra. We give a faithful action of the modular group PSL₂(Z) on Δ as a group of automorphisms. We give a linear basis for Δ. We describe the center of Δ and the 2-sided ideal Δ[Δ,Δ]Δ. We discuss how Δ is related to the q-Onsager algebra. |
| format |
Article |
| author |
Terwilliger, P. |
| spellingShingle |
Terwilliger, P. The Universal Askey-Wilson Algebra Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Terwilliger, P. |
| author_sort |
Terwilliger, P. |
| title |
The Universal Askey-Wilson Algebra |
| title_short |
The Universal Askey-Wilson Algebra |
| title_full |
The Universal Askey-Wilson Algebra |
| title_fullStr |
The Universal Askey-Wilson Algebra |
| title_full_unstemmed |
The Universal Askey-Wilson Algebra |
| title_sort |
universal askey-wilson algebra |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147390 |
| citation_txt |
The Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 66 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT terwilligerp theuniversalaskeywilsonalgebra AT terwilligerp universalaskeywilsonalgebra |
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2025-07-11T02:00:15Z |
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2025-07-11T02:00:15Z |
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