Generic symmetries of the Laurent extension of quantum plane
  A list of generic $U_q(sl_2)$-module algebra structures on the Laurent polynomial algebra over the quantum plane with uncountably many isomorphism classes is produced. Also, a complete list of such structures is presented in which the action of Cartan generator of $U_q(sl_2)$ does not reduce to multiplying x and y (the generators of quantum plane) by constants. 
Sergey D. Sinel'shchikov
math.QA