On the structure of quantum affine superalgebra $U_v(A(0,2{)}^{(4)})$

Abstract

We research $U_v(A(0,2{)}^{(4)}{)}^{+}$ defined by quantum Serre relations, when $v$ is not a root of unity. We prove that $U_v(A(0,2{)}^{(4)}{)}^{+}$ is isomorphic to a Nichols algebra. In other words, it is equivalent to define $U_v(A(0,2{)}^{(4)}{)}^{+}$ by quantum Serre relations and by the radical of the bilinear form. We determine all the root multiplicities and give a PBW basis of $U_v(A(0,2{)}^{(4)}{)}^{+}$.