FRT presentation of classical Askey-Wilson algebras

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.

13 pp

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Cited by in corpus (9)

• The Askey-Wilson algebra and its avatars
• The alternating central extension of the $q$-Onsager algebra
• Generalised Onsager Algebra in Quantum Lattice Models
• Heun operator of Lie type and the modified algebraic Bethe ansatz
• Racah problems for the oscillator algebra, the Lie algebra ${\mathfrak{sl}}_n$, and multivariate Krawtchouk polynomials
• A conjecture concerning the $q$-Onsager algebra
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• The $q$-Onsager algebra and its alternating central extension
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra