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Zbl 0849.17011
Ogievetskij, O.; Schmidke, W.B.; Wess, J.; Zumino, B.
(Ogievetsky, O.)
$q$-deformed Poincaré algebra. (English)
[J] Commun. Math. Phys. 150, No.3, 495-518 (1992). ISSN 0010-3616; ISSN 1432-0916/e

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.

MSC 2000:: *17B37 Quantum groups and related deformations
46L85 Noncommutative topology
46L87 Noncommutative differential geometry
81R50 Quantum groups and related algebraic methods in quantum theory
16W30 Hopf algebras (assoc. rings and algebras)

Keywords: $q$-differential calculus; $q$-Minkowski space; $q$-derivatives; $q$-Lorentz generators; $q$-Poincaré algebra; real Laplacian; comultiplication; Hopf algebra

Cited in: Zbl 0871.17012

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