Maximally extended sl (2|2) as a quantum double

Abstract

We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(∣) 2 2 using Drinfeldʼs quantum double con struction. We are led to enlarging the algebra by additional generators corresponding to an sl(2) automorphism. For this maximally extended algebra we construct a consistent Hopf algebra structure where the extensions exhibit several uncommon features. We determine the corresponding universal R-matrix containing some non-standard functions. Curiously, this Hopf algebra has one extra deformation parameter for which the R-matrix does not factorize into products of exponentials.