Revisiting the Askey–Wilson algebra with the universal <i>R</i> -matrix of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mstyle> <mml:msub> <mml:mi>U</mml:mi> <mml:mi>q</mml:mi> </mml:msub> <mml:mo>(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>l</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mstyle> </mml:math>

Abstract

Abstract A description of the embedding of a centrally extended Askey–Wilson algebra, , in is given in terms of the universal R -matrix of . The generators of the centralizer of 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 under the embedding map by showing that they obey the relations. This is achieved by introducing a natural coaction also constructed with the help of the R -matrix.