The article is a continuation of Hu and Zhuang (2021), we construct another admissible quantum affine algebra ${\mathcal{U}}_q\left({\widehat{\mathfrak{sl}}}_2\right)$ of affine type $A_1^{\left(1\right)}$ with different defining structural constants and variant $q$-Serre relations, its present formulae of the quantum root vectors are more involved than those in Hu and Zhuang (2021). We prove that as Hopf algebras, ${\mathcal{U}}_q\left({\widehat{\mathfrak{sl}}}_2\right)$ is neither isomorphic to the standard quantum affine algebra $U_q\left({\widehat{\mathfrak{sl}}}_2\right)$ nor to the one ${\mathcal{U}}_q\left({\widehat{\mathfrak{sl}}}_2\right)$ constructed in Hu and Zhuang (2021). The new quantum affine algebra has also the quantum Weyl group as its automorphism subgroup, by which its quantum root vectors are well-characterized, and leads to a description of the Poincaré-Birkhoff–Witt basis in terms of the Chevalley generators.

本文是Hu和Zhuang（2021）的续篇，我们构造了另一个可容许的量子仿射代数 ${\mathcal{ü}}_q（{\widehat{\mathfrak{sl}}}_{\mathrm{2个}}）$ 仿射类型 ${\mathrm{一个}}_{\mathrm{1个}}^{（\mathrm{1个}）}$ 具有不同的定义结构常数和变体 $q$-Serre关系，它目前的量子根矢量公式比Hu和Zhuang（2021）中的公式涉及更多。我们证明，作为霍普夫代数，${\mathcal{ü}}_q（{\widehat{\mathfrak{sl}}}_{\mathrm{2个}}）$ 既不与标准量子仿射代数同构 ${ü}_q（{\widehat{\mathfrak{sl}}}_{\mathrm{2个}}）$ 也不是一个 ${\mathcal{ü}}_q（{\widehat{\mathfrak{sl}}}_{\mathrm{2个}}）$在胡和庄（2021）建造。新的量子仿射代数还具有量子Weyl基团作为其自同构子群，通过它很好地表征了其量子根矢量，并根据Chevalley生成器对Poincaré-Birkhoff-Witt基进行了描述。