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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147989 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862746576918675456 |
|---|---|
| author | Terwilliger, P. |
| author_facet | Terwilliger, P. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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).
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| first_indexed | 2025-12-07T20:46:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147989 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:46:32Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂) Terwilliger, P. |
| title | 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_short | 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) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147989 |
| work_keys_str_mv | AT terwilligerp theuniversalaskeywilsonalgebraandtheequitablepresentationofuqsl2 AT terwilligerp universalaskeywilsonalgebraandtheequitablepresentationofuqsl2 |