  Automorphisms of the infinite dimensional Onsager algebra are introduced.
Certain quotients of the Onsager algebra are formulated using a polynomial in
these automorphisms. In the simplest case, the quotient coincides with the
classical analog of the Askey-Wilson algebra. In the general case,
generalizations of the classical Askey-Wilson algebra are obtained. The
corresponding class of solutions of the non-standard classical Yang-Baxter
algebra are constructed, from which a generating function of elements in the
commutative subalgebra is derived. We provide also another presentation of the
Onsager algebra and of the classical Askey-Wilson algebras.
