On the Structure of Quantum Affine Superalgebra $U_{v}(\mathrm{A}(0,2)^{(4)})$

We study the quantum affine superalgebra U_{v}(\mathrm{A}(0,2)^{(4)}) defined abstractly by Yamane, when v is not a root of unity. We prove that the defining relations satisfied by the Chevalley generators of U_{v}^{+}(\mathrm{A}(0,2)^{(4)}) , or equivalently the corresponding Nichols algebra B(\mathbb{V}) , are the quantum Serre relations, which means the Drinfeld–Jimbo-type realization of U_{v}(\mathrm{A}(0,2)^{(4)}) is obtained. Based on Lyndon word theory, we construct distinguished imaginary root vectors and give an estimation of their comultiplication in the form of generating functions. With these results, we determine all the root multiplicities and give a PBW basis of U_{v}^{+}(\mathrm{A}(0,2)^{(4)}) . We also describe concretely all the commutation relations among real root vectors and distinguished imaginary root vectors using generating functions, i.e., the Drinfeld second realization is obtained for U_{v}^{+}(\mathrm{A}(0,2)^{(4)}) .