The Laurent Extension of Quantum Plane: a Complete List of Uq(sl₂)-Symmetries

Abstract

This work finishes a classification of Uq(sl₂)-symmetries on the Laurent extension Cq[x±¹,y±¹] of the quantum plane. After reproducing the partial results of a previous paper of the author related to symmetries with non-trivial action of the Cartan generator(s) of Uq(sl₂) and the generic symmetries, a complete collection of non-generic symmetries is presented. Together, these collections constitute a complete list of Uq(sl₂)-symmetries on Cq[x±¹,y±¹].