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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2011 |
| Main Author: | |
| 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/123456789/147390 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712596663107584 |
|---|---|
| author | Terwilliger, P. |
| author_facet | Terwilliger, P. |
| citation_txt | The Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 66 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T17:38:01Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147390 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:38:01Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | The Universal Askey-Wilson Algebra Terwilliger, P. |
| title | 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_short | The Universal Askey-Wilson Algebra |
| title_sort | universal askey-wilson algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147390 |
| work_keys_str_mv | AT terwilligerp theuniversalaskeywilsonalgebra AT terwilligerp universalaskeywilsonalgebra |