FRT presentation of classical Askey-Wilson algebras

TL;DR

This paper introduces automorphisms of the Onsager algebra, constructs quotients related to the Askey-Wilson algebra, and explores their solutions within the classical Yang-Baxter framework, providing new algebraic presentations.

Contribution

It presents a novel approach to automorphisms and quotients of the Onsager algebra, generalizing the classical Askey-Wilson algebra and linking it to solutions of the classical Yang-Baxter algebra.

Findings

Automorphisms of the Onsager algebra are introduced.

Quotients related to the classical Askey-Wilson algebra are formulated.

Solutions to the classical Yang-Baxter algebra are constructed.

Abstract

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.