Algebra embedding of \(U_{q}(sl(2))\) into the tensor product of two \((q,h)\)-Weyl algebras. (Q899577)

Let \(q,h\) be complex numbers. Complex deformed \((q,h)\)-Weyl algebra \(W_{(q,h)}\) is the unital algebra generated by the operators \(X,S,S^{-1},\mu^{-1}\) subject to defining relations \[ SX=(qX+h)S,\quad SS^{-1}=S^{-1}S=1,\quad ((q-1)X+h)\mu^{-1}=\mu^{-1}((q -1)X+h)=1. \] Suppose that \(q\neq 1\). It is shown that \(U_q(2,\mathbb C)\) is embedded in the tensor square of \(W_{(q,h)}\). There is given an explicit form of this embedding.