The q-Onsager Algebra and the Universal Askey-Wilson Algebra

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Terwilliger, P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209528
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...