On generators and defining relations of quantum affine superalgebra Uq(𝔰𝔩̂m|n)

Abstract

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 [Formula: see text] associated to type [Formula: see text] and define a simple algebra [Formula: see text] generated by only a finite part of these sequences of quantum affine superalgebra [Formula: see text]. We show that the algebra [Formula: see text] is isomorphic to the quantum affine superalgebra [Formula: see text]. Using the above isomorphism, we prove there exists an isomorphism between the two realizations.