The Laurent Extension of Quantum Plane: a Complete List of $U_q({\mathfrak{sl}}_2)$-Symmetries

Abstract

This work finishes a classification of $U_q({\mathfrak{sl}}_2)$-symmetries on the Laurent extension ${\mathbb{C}}_q[x^{\pm 1},y^{\pm 1}]$ 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 $U_q({\mathfrak{sl}}_2)$ and the generic symmetries, a complete collection of non-generic symmetries is presented. Together, these collections constitute a complete list of $U_q({\mathfrak{sl}}_2)$-symmetries on ${\mathbb{C}}_q[x^{\pm 1},y^{\pm 1}]$.

References in corpus (1)

• Classification of U_q(sl_2)-module algebra structures on the quantum plane

Cited by in corpus (1)

• $U_q\left({\mathfrak{sl}}_2\right)$-symmetries of the quantum disc: a complete list