A note on the algebra Uq(sl2)

Abstract

Let $\mathbb{F}$ denote a field with characteristic not 2 and fix a nonzero $q\in \mathbb{F}$ such that $q^2\ne 1$. Let $U_q(s{l}_2)$ be the quantum enveloping algebra over $\mathbb{F}$ and let $x,y^{\pm 1},z$ be its equitable generators. Denote by $U_q^{\vee }$ the subalgebra of $U_q(s{l}_2)$ generated by $x,y^{-1},z$. In this paper, we solve two open problems concerning $U_q(s{l}_2)$ and $U_q^{\vee }$, respectively, which are proposed by Bockting-Conrad and Terwilliger.

Keywords:

• Center
• decomposition
• equitable presentation
• ideal
• quantum enveloping algebra

2010 MATHEMATICS Subject Classification:

• 17B37
• 08A05

Additional information

Funding

This work was supported by the NSF of China (No. 11471097).