Two-Parameter Quantum Groups and Drinfel'd Doubles

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We investigate two-parameter quantum groups corresponding to the general linear and special linear Lie algebras glₙ and slₙ. We show that these quantum groups can be realized as Drinfel'd doubles of certain Hopf subalgebras with respect to Hopf pairings. Using the Hopf pairing, we construct a corresponding R-matrix and a quantum Casimir element. We discuss isomorphisms among these quantum groups and connections with multiparameter quantum groups.