FRT presentation of classical Askey–Wilson algebras

2018/06/19 by Pascal Baseilhac, Nicolas Crampe, Nicolas Crampé
Computer Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Automorphism #Class (philosophy) #Computer science #Mathematics #Matrix Theory and Algorithms #Pure mathematics #Quotient #Quotient algebra #Subalgebra #math-ph #math.MP #math.QA

paper · pdf · doi:10.1007/s11005-019-01182-y

13 pp

arxiv created 2018/06/19 · openalex publication_date 2019/04/27 · arxiv updated 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• “Hidden symmetry” of Askey-Wilson polynomials
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
• The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
• The q-Onsager Algebra and the Universal Askey-Wilson Algebra