On generators and defining relations of quantum affine superalgebra U_q(ŝl_m|_n)

Two presentations of quantum affine superalgebras were introduced by Yamane in [On defining relations of affine Lie superalgebras and affine quantized universal enveloping superalgebras, Publ. Res. Inst. Math. Sci. 35 (1999) 321–390], which were called Drinfeld–Jimbo realization and Drinfeld realization. Drinfeld realization contains infinite sequences of generators and relations. In this paper, we consider the Drinfeld realization of quantum affine superalgebra Uq(ŝl_m|_n) associated to type sl_m|_n and define a simple algebra U0(ŝl_m|_n) generated by only a finite part of these sequences of quantum affine superalgebra Uq(ŝl_m|_n). We show that the algebra U0(ŝl_m|_n) is isomorphic to the quantum affine superalgebra Uq(ŝl_m|_n). Using the above isomorphism, we prove there exists an isomorphism between the two realizations.