Morphisms from \(U_v(sl_2)\) to the rotation algebra \({\mathcal A}_\theta\) (Q1373706)

The author considers the quantum group \(U_v(sl_2)\) generated by four elements \(E\), \(F\), \(K\) and \(K^{-1}\) satisfying quadratic relations with a parameter \(v\), as in the Drinfeld-Jimbo approach. He shows that as associative algebras (not as Hopf algebras) there exists a morphism from \(U_v(sl_2)\) to the rotation algebra \({\mathcal A}\). This algebra \({\mathcal A}\) is generated by two invertible elements \(U\) and \(V\) subject to a single relation \(VU=\lambda UV\), where \(\lambda\) is a complex parameter with \(| \lambda| =1\).