Another admissible quantum affine algebra of type [formula omitted] with quantum Weyl group

Abstract

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