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arxiv: 1704.05093 · v2 · pith:3AN3ISHBnew · submitted 2017-04-17 · 🧮 math-ph · hep-th· math.MP· math.QA

Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincar\'e

classification 🧮 math-ph hep-thmath.MPmath.QA
keywords algebrakappa-poincartimescontractionepsilonq-deformedr-matrixsuperalgebra
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We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the corresponding q-deformed Hopf algebra and its universal R-matrix by means of contraction. We make the curious observation that the above algebra is related to kappa-Poincar\'e symmetry. When dropping the graded part psl(2|2) we find a novel one-parameter deformation of the 3D kappa-Poincar\'e algebra. Our construction also provides a concise exact expression for its universal R-matrix.

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