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arxiv: 1602.04988 · v1 · pith:7LVP4HMTnew · submitted 2016-02-16 · 🧮 math-ph · hep-th· math.MP· math.QA

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

classification 🧮 math-ph hep-thmath.MPmath.QA
keywords algebraextendedr-matrixcorrespondingdoublehopfmaximallyquantum
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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.

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