%0 Journal Article
%T Higher rank classical analogs of the Askey-Wilson algebra from the $sl_N$ Onsager algebra
%+ Institut Denis Poisson (IDP)
%+ Laboratoire Charles Coulomb (L2C)
%+ Instituto de Física de São Carlos (IFSC-USP)
%A Baseilhac, Pascal
%A Crampé, Nicolas
%A Pimenta, Rodrigo A.
%Z 13 pages
%< avec comité de lecture
%Z L2C:18-240
%@ 0022-2488
%J Journal of Mathematical Physics
%I American Institute of Physics (AIP)
%V 60
%N 8
%P 081703
%8 2019-08-14
%D 2019
%Z 1811.02763
%R 10.1063/1.5111292
%K Onsager algebras
%K Askey-Wilson algebra
%K Yang-Baxter algebra
%K Integrable systems
%Z MSC : 81R50; 81R10; 81U15
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Quantum Algebra [math.QA]
%Z Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Journal articles
%X The $sl_N$-Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the $sl_N$-Onsager algebra is given, its current algebra and commutative subalgebra are constructed. Certain quotients of the $sl_N$-Onsager algebra are then considered, which produce `classical' analogs of higher rank extensions of the Askey-Wilson algebra. As examples, the cases $N=3$ and $N=4$ are described in details.
%G English
%L hal-01926766
%U https://hal.science/hal-01926766
%~ UNIV-TOURS
%~ CNRS
%~ UNIV-ORLEANS
%~ L2C
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ IDP
%~ UM-2015-2021
%~ TEST3-HALCNRS