Revisiting the Askey–Wilson algebra with the universal R -matrix of Uq(su(2)) Auteur(s): Crampé N., Gaboriaud Julien, Vinet Luc, Zaimi Meri (Article) Publié: Journal Of Physics A: Mathematical And Theoretical, vol. 53 p.05LT01 (2020) Texte intégral en Openaccess : Ref HAL: hal-02890142_v1 Ref Arxiv: 1908.04806 DOI: 10.1088/1751-8121/ab604e Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: A description of the embedding of a centrally extended Askey–Wilson algebra, AW(3), in Uq(sl2) 3 is given in terms of the universal R-matrix of Uq(sl2). The generators of the centralizer of Uq(sl2) in its three-fold tensor product are naturally expressed through conjugations of Casimir elements with R. They are seen as the images of the generators of AW(3) under the embedding map by showing that they obey the AW(3) relations. This is achieved by introducing a natural coaction also constructed with the help of the R-matrix. |