  Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently
we introduced a central extension $\Delta$ of AW(3) called the universal
Askey-Wilson algebra. In this paper we discuss a connection between $\Delta$
and the quantum algebra $U_q(\mathfrak{sl}_2)$. Our main result is an algebra
injection from $\Delta$ into a relative of $U_q(\mathfrak{sl}_2)$; the relative
is obtained from $U_q(\mathfrak{sl}_2)$ by adjoining three mutually commuting
indeterminates. We describe the injection using the equitable presentation of
$U_q(\mathfrak{sl}_2)$
