FRT presentation of classical Askey–Wilson algebras

  • Pascal Baseilhac
  • Nicolas CrampéEmail author


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 is 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.


Onsager algebra Non-standard Yang–Baxter algebra Askey–Wilson algebras Integrable systems 

Mathematics Subject Classification

81R50 81R10 81U15 



We thank S. Belliard for discussions, and P. Terwilliger and A. Zhedanov for comments and suggestions. P.B. and N.C. are supported by C.N.R.S. N.C. thanks the IDP for hospitality, where part of this work has been done.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institut Denis-Poisson CNRS/UMR 7013Université de Tours - Université d’Orléans Parc de GrammontToursFrance
  2. 2.Laboratoire Charles Coulomb (L2C)Univ Montpellier, CNRSMontpellierFrance

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