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

Abstract

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).