Universal R-Matrix of Quantum Affine $${\mathfrak{gl}(1,1)}$$ gl ( 1 , 1 )

Abstract

The universal $R$-matrix of the quantum affine superalgebra associated to the Lie superalgebra $\mathfrak{gl}(1,1)$ is realized as the Casimir element of certain Hopf pairing, based on the explicit coproduct formula of all the Drinfeld loop generators.