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

TL;DR

This paper constructs a maximally extended quantum algebra of centrally extended sl(2|2), deriving its universal R-matrix with unique features, including an extra deformation parameter and non-factorizable structure.

Contribution

It introduces a maximally extended quantum-deformed sl(2|2) algebra with a novel Hopf structure and a universal R-matrix featuring uncommon properties.

Findings

Derived the universal R-matrix using Drinfeld's quantum double

Constructed a consistent Hopf algebra with additional generators

Identified an extra deformation parameter affecting R-matrix structure

Abstract

We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. 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.