Maximally extended sl(2|2), q-deformed d(2, 1;ϵ) and 3D kappa-Poincaré*In Honour of Petr P Kulish and Ludvig D Faddeev. (7th July 2017)

• Record Type: Journal Article
• Authors: Beisert, Niklas; Hecht, Reimar; Hoare, Ben
• Is Part Of: Journal of physics. Volume 50:Number 31(2017)
• Publication Date: 2017-07-07
• Subjects: quantum algebra -- kappa-Poincaré -- integrable models -- universal R-matrix -- exceptional superalgebra -- algebraic contraction; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa7a2f
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We show that the maximal extension s l ( 2 ) ⋉ p s l ( 2 | 2 ) ⋉ C 3 of the s l ( 2 | 2 ) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d ( 2, 1 ; ϵ ) × s l ( 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 p s l ( 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.