Another admissible quantum affine algebra of type A₁⁽¹⁾ with quantum Weyl group

The article is a continuation of Hu and Zhuang (2021), we construct another admissible quantum affine algebra U_q(sl̂₂) of affine type A₁⁽¹⁾ 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, U_q(sl̂₂) is neither isomorphic to the standard quantum affine algebra U_q(sl̂₂) nor to the one U_q(sl̂₂) 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.