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Revisiting the Askey–Wilson algebra with the universal R -matrix of Uq(su(2))

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02890142
Contributor : Nicolas Crampé Connect in order to contact the contributor
Submitted on : Monday, July 6, 2020 - 10:22:54 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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Nicolas Crampé, Julien Gaboriaud, Luc Vinet, Meri Zaimi. Revisiting the Askey–Wilson algebra with the universal R -matrix of Uq(su(2)). Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2020, 53 (5), pp.05LT01. ⟨10.1088/1751-8121/ab604e⟩. ⟨hal-02890142⟩

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