The Universal Askey-Wilson Algebra and the Equitable Presentation of Uq(sl₂)

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• ISSN: 1815-0659
• Main Author: Terwilliger, P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147989
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...