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

Abstract The article is a continuation of Hu and Zhuang (2021), we construct another admissible quantum affine algebra U q ( sl 2 ) of affine type A 1 ( 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 (0000). We prove that as Hopf algebras, U q ( sl 2 ) is neither isomorphic to the standard quantum affine algebra U q ( sl 2 ) nor to the one U q ( sl 2 ) 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 Poincare-Birkhoff–Witt basis in terms of the Chevalley generators.