  An explicit homomorphism that relates the elements of the infinite
dimensional non-Abelian algebra generating $O_q(\hat{sl_2})$ currents and the
standard generators of the $q-$Onsager algebra is proposed. Two straightforward
applications of the result are then considered: First, for the class of quantum
integrable models which integrability condition originates in the $q-$Onsager
spectrum generating algebra, the infinite $q-$deformed Dolan-Grady hierarchy is
derived - bypassing the transfer matrix formalism. Secondly, higher
Askey-Wilson relations that arise in the study of symmetric special functions
generalizing the Askey-Wilson $q-$orthogonal polynomials are proposed.
