Ogievetskij, O.; Schmidke, W. B.; Wess, J.; Zumino, B. \(q\)-deformed Poincaré algebra. (English) Zbl 0849.17011 Commun. Math. Phys. 150, No. 3, 495-518 (1992). Summary: The \(q\)-differential calculus for the \(q\)-Minkowski space is developed. The algebra of the \(q\)-derivatives with the \(q\)-Lorentz generators is found giving the \(q\)-deformation of the Poincaré algebra. The reality structure of the \(q\)-Poincaré algebra is given. The reality structure of the \(q\)-differentials is also found. The real Laplacian is constructed. Finally the comultiplication, counit and antipode for the \(q\)-Poincaré algebra are obtained making it a Hopf algebra. Cited in 1 ReviewCited in 68 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 46L85 Noncommutative topology 46L87 Noncommutative differential geometry 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 16W30 Hopf algebras (associative rings and algebras) (MSC2000) Keywords:\(q\)-differential calculus; \(q\)-Minkowski space; \(q\)-derivatives; \(q\)-Lorentz generators; \(q\)-Poincaré algebra; real Laplacian; comultiplication; Hopf algebra PDFBibTeX XMLCite \textit{O. Ogievetskij} et al., Commun. Math. Phys. 150, No. 3, 495--518 (1992; Zbl 0849.17011) Full Text: DOI References: [1] Faddeev, L.D., Reshetikhin, N.Yu., Takhatajan, L.A.: Quantization of Lie groups and Lie algebras (in Russian). Algebra i Analiz1, 178 (1989) [2] Manin, Yu.I.: Quantum Groups and Non-Commutative Geometry. Preprint Montreal University CRM-1561 (1988). · Zbl 0724.17006 [3] Wess, J., Zumino, B.: Covariant Differential Calculus on the Quantum Hyperplane. Nucl. Phys. B (Proc. Suppl.)18B, 302 (1990) · Zbl 0957.46514 [4] Wess, J., Differential Calculus on Quantum Planes and Applications. Talk given at Third Centenary Celebrations of the Mathematische Gesellschaft, March 1990, based on work with B. Zumino, preprint KA-THEP-1990-22 (1990) [5] Carow-Watamura, U., Schlieker, M., Scholl, M., Watamura, S.: Tensor Representation of the Quantum GroupSL q (2, C) and Quantum Minkowski Space. Z. Phys. C-Particles and Fields48, 159 (1990); A Quantum Lorentz Group. Int. J. Mod. Phys. A6, 3081 (1991) · Zbl 0736.17018 · doi:10.1007/BF01565619 [6] Podleś, P., Woronowicz, S.L.: Quantum Deformation of Lorentz Group. Mittag-Leffler Institute Report No. 20, 1988/1989 · Zbl 0703.22018 [7] Ogievetsky, O., Schmidke, W.B., Wess, J., Zumino, B.: forthcoming paper [8] Schmidke, W.B., Wess, J., Zumino, B.: Aq-deformed Lorentz Algebra. Z. Phys. C-Particles and Fields52, 471 (1991) · Zbl 0793.17005 · doi:10.1007/BF01559443 [9] Ogievetsky, O., Schmidke, W.B., Wess, J., Zumino, B.: Six Generatorq-deformed Lorentz Algebra. Lett. Math. Phys.23, 233 (1991) · Zbl 0745.16020 · doi:10.1007/BF01885501 [10] Lukierski, J., Ruegg, H., Nowicki, A., Tolstoy, V.N.:Q-Deformation of Poincaré Algebra. Preprint UGVA-DPT 1991/02-710 [11] Drinfeld, V.G.: Quantum Groups. Proc. Int. Congr. Math.1, 798 (1986) [12] Jimbo, M.: Aq-Difference Analogue ofU(g) and the Yang-Baxter Equation. Lett. Math. Phys.1, 63 (1985) · Zbl 0587.17004 · doi:10.1007/BF00704588 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.