A Connection Behind the Terwilliger Algebras of $H(D,2)$ and $\frac{1}{2}H(D,2)$

Hau-Wen Huang, Chia-Yi Wen

The universal enveloping algebra $U({\mathfrak{sl}}_2)$ of ${\mathfrak{sl}}_2$ is a unital associative algebra over $\mathbb{C}$ generated by $E,F,H$ subject to the relations \begin{ali…