Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré

Abstract

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-Poincaré symmetry. When dropping the graded part psl(2|2) we find a novel one-parameter deformation of the 3D kappa-Poincaré algebra. Our construction also provides a concise exact expression for its universal R-matrix.

25 pages

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• Nonlocal Symmetries and Factorized Scattering
• Boost generator in AdS_3 integrable superstrings for general braiding
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• (2-)Drinfel'd Double and (2-)BF Theory
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish