The q-Onsager Algebra and the Universal Askey-Wilson Algebra
Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the q-Onsager algebra Oq. They defined the PBW basis elements recursively, and it is obscure how to express them in closed form. To mitigate the difficulty, we bring in the universal Askey-Wilson algebra Δq. There is a natural algebr...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2018 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209528 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The q-Onsager Algebra and the Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 34 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862651447477272576 |
|---|---|
| author | Terwilliger, P. |
| author_facet | Terwilliger, P. |
| citation_txt | The q-Onsager Algebra and the Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 34 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the q-Onsager algebra Oq. They defined the PBW basis elements recursively, and it is obscure how to express them in closed form. To mitigate the difficulty, we bring in the universal Askey-Wilson algebra Δq. There is a natural algebra homomorphism ♮: Oq → Δq. We apply ♮ to the above PBW basis, and express the images in closed form. Our results make heavy use of the Chebyshev polynomials of the second kind.
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| first_indexed | 2025-12-07T14:41:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209528 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T14:41:29Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Terwilliger, P. 2025-11-24T10:42:15Z 2018 The q-Onsager Algebra and the Universal Askey-Wilson Algebra / P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 34 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D80; 17B40 arXiv: 1801.06083 https://nasplib.isofts.kiev.ua/handle/123456789/209528 https://doi.org/10.3842/SIGMA.2018.044 Recently Pascal Baseilhac and Stefan Kolb obtained a PBW basis for the q-Onsager algebra Oq. They defined the PBW basis elements recursively, and it is obscure how to express them in closed form. To mitigate the difficulty, we bring in the universal Askey-Wilson algebra Δq. There is a natural algebra homomorphism ♮: Oq → Δq. We apply ♮ to the above PBW basis, and express the images in closed form. Our results make heavy use of the Chebyshev polynomials of the second kind. The author thanks Pascal Baseilhac and Samuel Belliard for giving this paper a close reading and offering valuable suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The q-Onsager Algebra and the Universal Askey-Wilson Algebra Article published earlier |
| spellingShingle | The q-Onsager Algebra and the Universal Askey-Wilson Algebra Terwilliger, P. |
| title | The q-Onsager Algebra and the Universal Askey-Wilson Algebra |
| title_full | The q-Onsager Algebra and the Universal Askey-Wilson Algebra |
| title_fullStr | The q-Onsager Algebra and the Universal Askey-Wilson Algebra |
| title_full_unstemmed | The q-Onsager Algebra and the Universal Askey-Wilson Algebra |
| title_short | The q-Onsager Algebra and the Universal Askey-Wilson Algebra |
| title_sort | q-onsager algebra and the universal askey-wilson algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209528 |
| work_keys_str_mv | AT terwilligerp theqonsageralgebraandtheuniversalaskeywilsonalgebra AT terwilligerp qonsageralgebraandtheuniversalaskeywilsonalgebra |