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

Abstract

This work finishes a classification of U q (sl 2 )-symmetries on the Laurent extension C q 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 U q (sl 2 ) and the generic symmetries, a complete collection of non-generic symmetries is presented. Together, these collections constitute a complete list of U q (sl 2 )-symmetries on C q x ±1 , y ±1 .