%0 Journal Article
%T FRT presentation of classical Askey–Wilson algebras
%+ Institut Denis Poisson (IDP)
%+ Laboratoire Charles Coulomb (L2C)
%A Baseilhac, Pascal
%A Crampé, Nicolas
%< avec comité de lecture
%@ 0377-9017
%J Letters in Mathematical Physics
%I Springer Verlag
%V 109
%P 2187–2207
%8 2019
%D 2019
%Z 1806.07232
%R 10.1007/s11005-019-01182-y
%K Onsager algebra
%K Non-standard Yang-Baxter algebra
%K Askey-Wilson algebras
%K Integrable systems
%Z MSC: 81R50; 81R10; 81U15
%Z Mathematics [math]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Quantum Algebra [math.QA]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-02152774/document
%2 https://hal.science/hal-02152774/file/1806.07232.pdf
%L hal-02152774
%U https://hal.science/hal-02152774
%~ UNIV-TOURS
%~ CNRS
%~ UNIV-ORLEANS
%~ INSMI
%~ L2C
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ IDP
%~ UM-2015-2021
%~ TEST3-HALCNRS