Freidel-Maillet type presentations of $U_q(sl_2)$

TLDR: In this paper, a unified framework for the Chevalley and equitable presentation of $U_q(sl_2)$ is introduced, given in terms of a system of Freidel-Maillet type equations satisfied by a pair of quantum K-operators, whose entries are expressed in terms either CHs or equitable generators.

Abstract: A unified framework for the Chevalley and equitable presentation of $U_q(sl_2)$ is introduced. It is given in terms of a system of Freidel-Maillet type equations satisfied by a pair of quantum K-operators ${\cal K}^\pm$, whose entries are expressed in terms of either Chevalley or equitable generators. The Hopf algebra structure is reconsidered in light of this presentation, and interwining relations for K-operators are obtained. A K-operator solving a spectral parameter dependent Freidel-Maillet equation is also considered. Specializations to $U_q(sl_2)$ admit a decomposition in terms of ${\cal K}^\pm$. Explicit examples of K-matrices are constructed.