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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147390 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 66 назв. — англ. |
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Terwilliger, P. 2019-02-14T16:59:45Z 2019-02-14T16:59:45Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/147390 DOI:10.3842/SIGMA.2011.069 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. This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available a thttp://www.emis.de/journals/SIGMA/OPSF.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Universal Askey-Wilson Algebra Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The Universal Askey-Wilson Algebra |
| spellingShingle |
The Universal Askey-Wilson Algebra Terwilliger, P. |
| 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 |
| 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 |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
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AT terwilligerp theuniversalaskeywilsonalgebra AT terwilligerp universalaskeywilsonalgebra |
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2025-12-07T17:38:01Z |
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2025-12-07T17:38:01Z |
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1850871991560568832 |