On the Structure of Quantum Toroidal Superalgebra E_m|n

Recently the quantum toroidal superalgebra E_m|n associated with 𝔤𝔩_m|n was introduced by L. Bezerra and E. Mukhin, which is not a quantum Kac–Moody algebra. The quantum toroidal superalgebra E_m|n exploits infinite sequences of generators and relations of the form, which are called Drinfeld realization. In this paper, we use only finite set of generators and relations to define an associative algebra E_m|n^' and show that there exists an epimorphism from E_m|n^' to the quantum toroidal superalgebra E_m|n . In particular, the structure of E_m|n^' enjoys some properties like Drinfeld–Jimbo realization.